Solving Ratio Word Problems

Solving word problems on ratio with a bar model: match the amount you know to the number of units it stands for, find 1 unit, then answer what is asked.

Before you start

A ratio can be drawn as a bar model. For $3 : 5$ , draw a bar of 3 equal units and a bar of 5 equal units. Every unit in the drawing stands for the same amount. In this lesson a "unit" is one of these equal parts. A centimetre or a kilogram is called a unit of measurement.

When a known total is divided in a given ratio, the total stands for all the units together. Mei Ling and Ravi share $72 in the ratio $3 : 5$ . There are $3 + 5 = 8$ units, so 8 units = $72 and 1 unit = $9. Mei Ling gets $3 \times 9 = 27$ dollars and Ravi gets $5 \times 9 = 45$ dollars.

Units can be counted only when the terms of the ratio are whole numbers. A ratio with fractions is multiplied through by the LCM of the denominators, and a ratio with decimals by 10, 100 or 1000. Quantities in different units of measurement are changed to the same one first. A ratio with whole-number terms is easier to draw in its simplest form: divide its terms by their HCF.

Match the Known Amount to Its Units

A ratio by itself gives no amounts. The ratio $3 : 5$ says only that one bar has 3 units and the other has 5. To find an amount, a problem must also give one amount, and you must decide how many units that amount stands for. Then you can find the value of 1 unit, and every other amount follows from it.

The amount given is not always the total. It may be one of the quantities, or the difference between two of them, or two quantities out of three added together. Read which it is, and mark it on the bar model in the right place.

How many units the known amount stands for

The question gives	Match it to	Example
one quantity	the units of that quantity's own bar	in $3 : 5$ , the first quantity is 3 units
the total	all the units together	in $3 : 5$ , the total is $3 + 5 = 8$ units
the difference	the extra units of the longer bar	in $3 : 5$ , the difference is $5 - 3 = 2$ units
two quantities out of three, added together	the units of those two bars together	in $2 : 3 : 7$ , the first two make $2 + 3 = 5$ units

Method: four steps

Draw. Draw a bar for each quantity, with as many equal units as its term of the ratio. Write each amount you know where it belongs, and put "?" on what you must find.
Match. Write down how many units the known amount stands for, as in "5 units = $225".
Find 1 unit. Divide the known amount by its number of units.
Answer and check. Multiply the value of 1 unit by the number of units in what is asked. Then check that your amounts fit every fact in the question: they are in the ratio given, and they give back the amount that was given.

One Quantity Is Known

In the simplest problems the question gives the amount of one quantity. That amount matches the units of its own bar: not the other bar, and not all the units together.

Example 1: One quantity known, the other wanted

Hui Min and Ravi shared a cash prize in the ratio $5 : 6$ . Hui Min received $225. How much did Ravi receive?

Solution

Draw. Hui Min is named first, so her bar has 5 units and Ravi's bar has 6 units. The $225 is Hui Min's, so it is written beside her bar.

Match. Hui Min's bar is 5 units, so 5 units = $225.

Find 1 unit. $225 \div 5 = 45$ , so 1 unit = $45.

Answer. Ravi's bar is 6 units: $6 \times 45 = 270$ .

Check. $225 : 270 = 5 : 6$ , on dividing both terms by 45. The two amounts are in the ratio given.

Equivalent ratios give the same answer: $5 : 6 = 225 : 270$ , each term multiplied by 45. The value of 1 unit is that multiplier.

Ravi received $270.

Example 2: One quantity known, the total wanted

In a school choir, the ratio of the number of boys to the number of girls is $4 : 7$ . There are 28 girls. How many students are in the choir?

Solution

Draw. The boys' bar has 4 units and the girls' bar has 7 units. The 28 is written beside the girls' bar. The question asks for the whole choir, so the "?" is on the bracket round both bars.

Match. The 28 is the number of girls only, so 7 units = 28. It is not $4 + 7 = 11$ units: that would be the whole choir, which is not known.

Find 1 unit. $28 \div 7 = 4$ , so 1 unit = 4 students.

Answer. The whole choir is $4 + 7 = 11$ units: $11 \times 4 = 44$ .

Check. There are $4 \times 4 = 16$ boys, and $16 + 28 = 44$ . Also $16 : 28 = 4 : 7$ , on dividing both terms by 4.

There are 44 students in the choir.

The Difference Is Known

Some problems give neither quantity. They say how much more one is than the other. On a bar model the two bars are equal as far as the end of the shorter one, and the difference is the part of the longer bar that goes beyond it. So the difference matches the extra units: the larger term of the ratio minus the smaller term.

Example 3: The difference known, both quantities and the total wanted

One Saturday at a hawker centre, the ratio of the money taken by the drinks stall to the money taken by the chicken rice stall was $5 : 7$ . The chicken rice stall took $560 more than the drinks stall.
(a) How much did each stall take?
(b) How much did the two stalls take altogether?

Solution

Draw. The drinks stall's bar has 5 units and the chicken rice stall's bar has 7 units. The $560 is not either bar. It is the part of the longer bar that goes beyond the shorter one, so it is marked over those extra units.

Match. The extra part is $7 - 5 = 2$ units, so 2 units = $560.

Find 1 unit. $560 \div 2 = 280$ , so 1 unit = $280.

(a) Drinks stall: $5 \times 280 = 1400$ . Chicken rice stall: $7 \times 280 = 1960$ .

(b) The two bars together are $5 + 7 = 12$ units: $12 \times 280 = 3360$ .

Check. $1960 - 1400 = 560$ , the difference given. $1400 : 1960 = 5 : 7$ , on dividing both terms by 280. And $1400 + 1960 = 3360$ .

(a) The drinks stall took $1400 and the chicken rice stall took $1960.
(b) The two stalls took $3360 altogether.

Example 4: The difference has to be found first

The ratio of Siti's mass to her father's mass is $5 : 7$ . Her brother's mass is 13 kg more than Siti's mass and 9 kg less than their father's mass. Find Siti's mass.

Solution

Draw. Siti's bar has 5 units and her father's bar has 7 units. Her brother is heavier than Siti and lighter than their father, so his bar ends between the ends of theirs. It need not be a whole number of units, so it is drawn in one piece.

From the end of Siti's bar to the end of her brother's bar is 13 kg. From there to the end of their father's bar is 9 kg more. So their father is $13 + 9 = 22$ kg heavier than Siti.

Match. That difference is the $7 - 5 = 2$ extra units of the father's bar, so 2 units = 22 kg.

Find 1 unit. $22 \div 2 = 11$ , so 1 unit = 11 kg.

Answer. Siti's bar is 5 units: $5 \times 11 = 55$ .

Check. Her father's mass is $7 \times 11 = 77$ kg, and $55 : 77 = 5 : 7$ , on dividing both terms by 11. Her brother's mass is $55 + 13 = 68$ kg, and it is also $77 - 9 = 68$ kg, so both facts about him hold.

Siti's mass is 55 kg.

The Total Is Known and the Difference Is Wanted

When the total is known, it matches all the units together, just as when a quantity is divided in a given ratio. But the question may not ask for the two shares. If it asks how many more one quantity is than the other, the answer is the value of the extra units, and the two quantities need not be found first.

Example 5: The total known, the difference wanted

Ali and Ravi scored 33 goals altogether in a football season. The ratio of the number of goals Ali scored to the number of goals Ravi scored is $5 : 6$ . How many more goals did Ravi score than Ali?

Solution

Draw. Ali's bar has 5 units and Ravi's bar has 6 units. The 33 is both bars together, so it is on the bracket. The "?" is over the part of Ravi's bar that goes beyond Ali's.

Match. Both bars together are $5 + 6 = 11$ units, so 11 units = 33.

Find 1 unit. $33 \div 11 = 3$ , so 1 unit = 3 goals.

Answer. Ravi's bar is $6 - 5 = 1$ unit longer than Ali's, and 1 unit is 3 goals.

Check. Ali scored $5 \times 3 = 15$ goals and Ravi scored $6 \times 3 = 18$ goals. $15 + 18 = 33$ , the total given. $15 : 18 = 5 : 6$ , on dividing both terms by 3. And $18 - 15 = 3$ .

Ravi scored 3 more goals than Ali.

Three Quantities

With three quantities there are three bars, and the method does not change. The known amount may be one bar, all three bars, two of the bars added together, or the difference between two of them. Count only the units of the bars that the known amount speaks of.

Example 6: Three quantities, the sum of two known

Ali, Siti and Ravi collect stickers. The numbers of stickers they have are in the ratio $2 : 3 : 7$ . Ali and Siti have 60 stickers altogether. How many stickers does Ravi have?

Solution

Draw. Ali's bar has 2 units, Siti's has 3 units and Ravi's has 7 units. The 60 is Ali's bar and Siti's bar together, so the bracket goes round those two bars only.

Match. Ali and Siti together are $2 + 3 = 5$ units, so 5 units = 60.

Find 1 unit. $60 \div 5 = 12$ , so 1 unit = 12 stickers.

Answer. Ravi's bar is 7 units: $7 \times 12 = 84$ .

Check. Ali has $2 \times 12 = 24$ stickers and Siti has $3 \times 12 = 36$ , and $24 + 36 = 60$ . Also $24 : 36 : 84 = 2 : 3 : 7$ , on dividing every term by 12.

Ravi has 84 stickers.

Example 7: Three quantities, the difference of two known

Mrs Goh's class grows chilli, tomato and brinjal plants in the school garden. The numbers of chilli, tomato and brinjal plants are in the ratio $3 : 5 : 8$ . There are 15 more brinjal plants than tomato plants. How many plants are there altogether?

Solution

Draw. The chilli bar has 3 units, the tomato bar has 5 units and the brinjal bar has 8 units. The 15 is the part of the brinjal bar that goes beyond the tomato bar. The "?" is on the bracket round all three bars.

Match. The brinjal bar is $8 - 5 = 3$ units longer than the tomato bar, so 3 units = 15.

Find 1 unit. $15 \div 3 = 5$ , so 1 unit = 5 plants.

Answer. The three bars together are $3 + 5 + 8 = 16$ units: $16 \times 5 = 80$ .

Check. There are $3 \times 5 = 15$ chilli plants, $5 \times 5 = 25$ tomato plants and $8 \times 5 = 40$ brinjal plants. $40 - 25 = 15$ , the difference given. $15 : 25 : 40 = 3 : 5 : 8$ , on dividing every term by 5. And $15 + 25 + 40 = 80$ .

There are 80 plants altogether.

When the Ratio Must Be Made Ready First

A bar is drawn in whole units, so the terms of the ratio must be whole numbers before you draw. One of three things may have to be done first.

Put the ratio in its simplest form. A ratio of $18 : 30$ could be drawn as 18 units and 30 units, and the method would still work. Dividing both terms by their HCF, 6, gives $3 : 5$ , which is much easier to draw and to count.
Clear fractions and decimals. Multiply every term by the LCM of the denominators, or by 10, 100 or 1000 for decimals. For example, $\frac{2}{3} : \frac{1}{2}$ becomes $4 : 3$ when both terms are multiplied by 6.
Use the same unit of measurement. The ratio of 750 ml to 2 litres is not $750 : 2$ . Change 2 litres to 2000 ml first: $750 : 2000 = 3 : 8$ .

Each of these gives an equivalent ratio, so the quantities are still compared in exactly the same way.

Example 8: A ratio with fractions

Mei Ling makes a fruit drink by mixing orange juice and mango juice in the ratio $\frac{2}{3} : \frac{1}{2}$ . She uses 240 ml of orange juice. How much mango juice does she use?

Solution

Make the ratio ready. The denominators are 3 and 2, and their LCM is 6. Multiply both terms by 6: $\frac{2}{3} \times 6 : \frac{1}{2} \times 6 = 4 : 3$ .

Draw. The orange juice bar has 4 units and the mango juice bar has 3 units. The 240 ml is the orange juice.

Match. 4 units = 240 ml.

Find 1 unit. $240 \div 4 = 60$ , so 1 unit = 60 ml.

Answer. The mango juice is 3 units: $3 \times 60 = 180$ .

Check. $240 : 180 = 4 : 3$ , on dividing both terms by 60, and $4 : 3$ is the ratio $\frac{2}{3} : \frac{1}{2}$ written in whole numbers.

Mei Ling uses 180 ml of mango juice.

Example 9: Quantities in different units of measurement

To mix a shade of blue, Mr Tan uses 750 ml of white paint for every 2 litres of blue paint. To paint a classroom he uses 2.4 litres of white paint. How much blue paint does he use?

Solution

Make the ratio ready. The two amounts must be in the same unit of measurement. $2\text{ litres} = 2000\text{ ml}$ , so the ratio of white paint to blue paint is $750 : 2000$ . The HCF of 750 and 2000 is 250, and dividing both terms by 250 gives $3 : 8$ .

Draw. The white paint bar has 3 units and the blue paint bar has 8 units. The 2.4 litres is the white paint.

Match. 3 units = 2.4 litres. Here a "unit" is one equal part of a bar. The unit of measurement is the litre.

Find 1 unit. $2.4 \div 3 = 0.8$ , so 1 unit = 0.8 litres.

Answer. The blue paint is 8 units: $8 \times 0.8 = 6.4$ .

Check. $2.4 : 6.4 = 24 : 64 = 3 : 8$ , on multiplying both terms by 10 and then dividing both by 8. That is the ratio of 750 ml to 2000 ml.

Mr Tan uses 6.4 litres of blue paint.

Common Mistakes

Matching the known amount to the wrong bar. In Example 1 the $225 is Hui Min's, and Hui Min's term is 5. Writing "6 units = $225" puts Hui Min's money on Ravi's bar. It gives 1 unit = $37.50 and leaves Hui Min with $5 \times 37.50 = 187.50$ dollars, not the $225 the question gives. Write a name beside each bar before you write any amount.
Taking the total number of units when only one quantity is given. In Example 2 the 28 is the number of girls, which is 7 units. Writing "11 units = 28" treats 28 as the whole choir. Add the terms only when the amount you know is the total.
Matching a difference to a whole bar. In Example 3 the $560 is how much more one stall took than the other, so it is $7 - 5 = 2$ units. It is not 7 units, and it is not 12 units.
Forgetting to answer the question asked. Example 5 asks how many more goals Ravi scored, so the answer is 3 goals, not "15 goals and 18 goals". Read the question again before you write your answer.
Counting units before the ratio is ready. The ratio of 45 minutes to 1 hour is not $45 : 1$ . In minutes it is $45 : 60 = 3 : 4$ , so the bars have 3 units and 4 units.

Practice

Work each question on paper, with a bar model, before you open its solution.

Question 1

The ratio of Ali's weekly pocket money to Mei Ling's weekly pocket money is $3 : 4$ . Ali gets $21 a week. How much does Mei Ling get a week?

ShowHide solution

Ali's bar has 3 units and Mei Ling's bar has 4 units. The $21 is Ali's.

3 units = $21. $21 \div 3 = 7$ , so 1 unit = $7.

Mei Ling's bar is 4 units: $4 \times 7 = 28$ .

Check: $21 : 28 = 3 : 4$ , on dividing both terms by 7.

Mei Ling gets $28 a week.

Question 2

A car park has only cars and motorcycles in it. The ratio of the number of cars to the number of motorcycles is $9 : 2$ . There are 16 motorcycles. How many vehicles are in the car park altogether?

ShowHide solution

The cars' bar has 9 units and the motorcycles' bar has 2 units. The 16 is the motorcycles only. The "?" is on the bracket round both bars.

2 units = 16. $16 \div 2 = 8$ , so 1 unit = 8 vehicles.

The two bars together are $9 + 2 = 11$ units: $11 \times 8 = 88$ .

Check: there are $9 \times 8 = 72$ cars, and $72 + 16 = 88$ . Also $72 : 16 = 9 : 2$ , on dividing both terms by 8.

There are 88 vehicles in the car park.

Question 3

Siti's recipe for 2 cakes uses 300 g of butter. In the recipe, the ratio of the mass of butter to the mass of flour is $3 : 7$ . Find the mass of flour needed for one cake.

ShowHide solution

The question asks about one cake, so first find the butter in one cake: $300 \div 2 = 150$ , so one cake uses 150 g of butter.

The butter bar has 3 units and the flour bar has 7 units. The 150 g is the butter in one cake.

3 units = 150 g. $150 \div 3 = 50$ , so 1 unit = 50 g.

The flour is 7 units: $7 \times 50 = 350$ .

Check: $150 : 350 = 3 : 7$ , on dividing both terms by 50.

Working with both cakes gives the same answer: 3 units = 300 g, so 1 unit = 100 g and the flour for two cakes is $7 \times 100 = 700$ g. Half of that is 350 g.

One cake needs 350 g of flour.

Question 4

The ratio of Ravi's height to his little sister's height is $8 : 5$ . Ravi is 54 cm taller than his sister. Find the height of each of them.

ShowHide solution

Ravi's bar has 8 units and his sister's bar has 5 units. The 54 cm is the part of Ravi's bar that goes beyond his sister's.

The extra part is $8 - 5 = 3$ units, so 3 units = 54 cm. $54 \div 3 = 18$ , so 1 unit = 18 cm.

Ravi: $8 \times 18 = 144$ . His sister: $5 \times 18 = 90$ .

Check: $144 - 90 = 54$ , and $144 : 90 = 8 : 5$ , on dividing both terms by 18.

Ravi is 144 cm tall and his sister is 90 cm tall.

Question 5

In a school library, the ratio of the number of English books to the number of Chinese books is $9 : 4$ . There are 1250 more English books than Chinese books. How many English and Chinese books are there altogether?

ShowHide solution

The English bar has 9 units and the Chinese bar has 4 units. The 1250 is the part of the English bar that goes beyond the Chinese bar. The "?" is on the bracket round both bars.

The extra part is $9 - 4 = 5$ units, so 5 units = 1250. $1250 \div 5 = 250$ , so 1 unit = 250 books.

The two bars together are $9 + 4 = 13$ units: $13 \times 250 = 3250$ .

Check: there are $9 \times 250 = 2250$ English books and $4 \times 250 = 1000$ Chinese books. $2250 - 1000 = 1250$ , the difference given, and $2250 + 1000 = 3250$ .

There are 3250 English and Chinese books altogether.

Question 6

Mr Tan's fruit stall has 180 apples and oranges altogether. The ratio of the number of apples to the number of oranges is $7 : 5$ . How many more apples than oranges are there?

ShowHide solution

The apples' bar has 7 units and the oranges' bar has 5 units. The 180 is both bars together. The "?" is on the part of the apples' bar that goes beyond the oranges' bar.

Both bars together are $7 + 5 = 12$ units, so 12 units = 180. $180 \div 12 = 15$ , so 1 unit = 15 fruits.

The apples' bar is $7 - 5 = 2$ units longer: $2 \times 15 = 30$ .

Check: there are $7 \times 15 = 105$ apples and $5 \times 15 = 75$ oranges. $105 + 75 = 180$ , the total given, and $105 - 75 = 30$ .

There are 30 more apples than oranges.

Question 7

A bag holds red, blue and green marbles. The numbers of red, blue and green marbles are in the ratio $5 : 2 : 4$ . There are 42 blue and green marbles altogether. How many red marbles are there?

ShowHide solution

The red bar has 5 units, the blue bar has 2 units and the green bar has 4 units. The 42 is the blue bar and the green bar together, so the bracket goes round those two bars only.

Blue and green together are $2 + 4 = 6$ units, so 6 units = 42. $42 \div 6 = 7$ , so 1 unit = 7 marbles.

The red bar is 5 units: $5 \times 7 = 35$ .

Check: there are $2 \times 7 = 14$ blue marbles and $4 \times 7 = 28$ green marbles, and $14 + 28 = 42$ . Also $35 : 14 : 28 = 5 : 2 : 4$ , on dividing every term by 7.

There are 35 red marbles.

Question 8

Ali, Siti and Hui Min share the cost of a present for their teacher in the ratio $2 : 3 : 5$ . Hui Min pays $9 more than Siti. How much does the present cost?

ShowHide solution

Ali's bar has 2 units, Siti's has 3 units and Hui Min's has 5 units. The $9 is the part of Hui Min's bar that goes beyond Siti's. The "?" is on the bracket round all three bars.

The extra part is $5 - 3 = 2$ units, so 2 units = $9. $9 \div 2 = 4.5$ , so 1 unit = $4.50.

The three bars together are $2 + 3 + 5 = 10$ units: $10 \times 4.50 = 45$ .

Check: Ali pays $2 \times 4.50 = 9$ dollars, Siti pays $3 \times 4.50 = 13.50$ dollars and Hui Min pays $5 \times 4.50 = 22.50$ dollars. $22.50 - 13.50 = 9$ , the difference given, and $9 + 13.50 + 22.50 = 45$ .

The present costs $45.

Question 9

At a school concert, the ratio of the number of adults to the number of children is $18 : 30$ . There are 96 more children than adults. How many people are at the concert?

ShowHide solution

Put the ratio in its simplest form first. The HCF of 18 and 30 is 6, so $18 : 30 = 3 : 5$ .

The adults' bar has 3 units and the children's bar has 5 units. The 96 is the part of the children's bar that goes beyond the adults' bar. The "?" is on the bracket round both bars.

The extra part is $5 - 3 = 2$ units, so 2 units = 96. $96 \div 2 = 48$ , so 1 unit = 48 people.

The two bars together are $3 + 5 = 8$ units: $8 \times 48 = 384$ .

Check: there are $3 \times 48 = 144$ adults and $5 \times 48 = 240$ children. $240 - 144 = 96$ , the difference given. $144 : 240 = 3 : 5$ , on dividing both terms by 48, and $3 : 5$ is $18 : 30$ in its simplest form.

There are 384 people at the concert.

Question 10

For a craft project, Siti uses 40 cm of red ribbon for every 1 m of blue ribbon. She uses 4.2 m more blue ribbon than red ribbon. Find the length of each colour of ribbon that she uses.

ShowHide solution

Use the same unit of measurement first. $1\text{ m} = 100\text{ cm}$ , so the ratio of red ribbon to blue ribbon is $40 : 100 = 2 : 5$ , on dividing both terms by 20.

The red bar has 2 units and the blue bar has 5 units. The 4.2 m is the part of the blue bar that goes beyond the red bar.

The extra part is $5 - 2 = 3$ units, so 3 units = 4.2 m. $4.2 \div 3 = 1.4$ , so 1 unit = 1.4 m.

Red: $2 \times 1.4 = 2.8$ . Blue: $5 \times 1.4 = 7$ .

Check: $7 - 2.8 = 4.2$ , the difference given. $2.8 : 7 = 28 : 70 = 2 : 5$ , on multiplying both terms by 10 and then dividing both by 14.

Siti uses 2.8 m of red ribbon and 7 m of blue ribbon.

Question 11

The ratio of the mass of parcel A to the mass of parcel B is $0.6 : 1.5$ . Parcel B is 2.7 kg heavier than parcel A. Find the mass of each parcel.

ShowHide solution

Make the terms whole numbers first. Multiply both terms by 10: $0.6 : 1.5 = 6 : 15$ . Then divide both terms by their HCF, 3: $6 : 15 = 2 : 5$ .

Parcel A's bar has 2 units and parcel B's bar has 5 units. The 2.7 kg is the part of parcel B's bar that goes beyond parcel A's.

The extra part is $5 - 2 = 3$ units, so 3 units = 2.7 kg. $2.7 \div 3 = 0.9$ , so 1 unit = 0.9 kg.

Parcel A: $2 \times 0.9 = 1.8$ . Parcel B: $5 \times 0.9 = 4.5$ .

Check: $4.5 - 1.8 = 2.7$ , the difference given. $1.8 : 4.5$ is the given ratio $0.6 : 1.5$ with both terms multiplied by 3, so it is equivalent to it.

The mass of parcel A is 1.8 kg and the mass of parcel B is 4.5 kg.

Question 12

The ratio of the number of stamps Hui Min has to the number of stamps Ali has is $4 : 9$ . Ravi has 35 more stamps than Hui Min and 40 fewer stamps than Ali.
(a) How many stamps does Hui Min have?
(b) How many stamps does Ravi have?

ShowHide solution

Hui Min's bar has 4 units and Ali's bar has 9 units. Ravi has more stamps than Hui Min and fewer than Ali, so his bar ends between the ends of theirs. It need not be a whole number of units, so it is drawn in one piece.

From the end of Hui Min's bar to the end of Ali's bar is $35 + 40 = 75$ stamps. That is the $9 - 4 = 5$ extra units of Ali's bar, so 5 units = 75. $75 \div 5 = 15$ , so 1 unit = 15 stamps.

(a) Hui Min's bar is 4 units: $4 \times 15 = 60$ .

(b) Ravi has 35 more stamps than Hui Min: $60 + 35 = 95$ .

Check: Ali has $9 \times 15 = 135$ stamps, and $135 - 40 = 95$ , which agrees with (b). Also $60 : 135 = 4 : 9$ , on dividing both terms by 15.

(a) Hui Min has 60 stamps.
(b) Ravi has 95 stamps.

Key Points

A ratio gives the number of units in each bar. One known amount is needed to find the value of 1 unit.
The method is draw, match, find 1 unit, answer and check.
One quantity known: it matches the units of its own bar.
The total known: it matches all the units together.
The difference known: it matches the extra units of the longer bar, which is the larger term minus the smaller term.
Three quantities: count only the units of the bars that the known amount speaks of.
Before you draw, make the terms of the ratio whole numbers: use the same unit of measurement, clear fractions and decimals, and put the ratio in its simplest form.
Answer the question that was asked, then check your answer against every fact in the question.