USING RATIOS TO DIVIDE QUANTITIES WORD PROBLEMS WORKSHEET

Problem 1 :

In an election, the votes cast for two of the candidates were in the ratio 5 : 7. If the successful candidate received 20734 votes, how many votes did his opponent receive?

Solution :

By observing the given ratio, the shares between two candidates are 5 : 7

Let x be the number of votes 1 share

number of votes got by winning candidate = 7x

number of votes cast by opponent = 5x

5x + 7x = 20734

12x = 20734

x = 20734/12

x = 1728

By applying the value of x, we get

7x = 7(1728) ==>12096

Number of votes cast by opponent candidate = 5x

= 5(1728)

= 8640

So, number of votes cast by winning candidate is 12096.

Problem 2 :

A car can travel 240 km in 15 liters of petrol. How much distance will it travel in 25 liters of petrol?

Solution :

Distance covered = 240 km

Petrol consumption = 15 liters

To find the distance covered using 1 liter of petrol, we have to divide 240 km by 15

= 240/15

= 16 km

We cover 16 km distance using 1 liter of petrol.

Problem 3 :

Bachhu Manjhi earns $24000 in 8 months. At this rate,

(a) how much does he earn in one year?

(b) in how many months does he earn $42000?

Solution :

Earning for 8 months = 24000

a) Earning for a year :

Earning for 1 month = 24000/8

= 3000

1 year = 12 months 

Earning for a year = 12(3000)

= 36000

(b) To find the number of months taken to earn $42000, let us consider the number of month be n

n(3000) = 36000

n = 36000/3000

n = 12

So, 12 month will be taken to earn 42000.

Problem 4 :

The yield of wheat from 8 hectares of land is 360 quintals. Find the number of hectares of land required for a yield of 540 quintals?

Solution :

Let x be the number of hectares of land required.

8 : 360 = x : 540

8/360 = x/540

Doing cross multiplication, we get

8(540) = x(360)

x = 8(540) / 360

x = 12

So, we need 12 hectares for a yield of 540 quintals.

Problem 5 :

The earth rotates 360^o about its axis in about 24 hours. By how much degree will it rotate in 2 hours?

Solution :

Degree measure in 1 hour, when earth rotates = 360/24

Degree measure for 2 hours = 2 x (360/24)

= 360/12

= 30

So, in 2 hours the earth rotates 30 degree 

Problem 6 :

Shivangi is suffering from anaemia as haemoglobin level in her blood is lower than the normal range. Doctor advised her to take one iron tablet two times a day. If the cost of 10 tablets is $ 17, then what amount will she be required to pay for her medical bill for 15 days?

Solution :

Cost of 10 tablets = $17

Cost of 1 tablet = 17/10

= $1.7

Number times he is taking tablet = 2

Number days of medication = 15 days

Number of tablet required = 15 x 2

= 30 tablets

Cost of 1 tablet = $1.7

Required cost = 1.7 x 30

= $51

Problem 7 :

The quarterly school fee in Kendriya Vidyalaya for Class VI is $540. What will be the fee for seven months? 

Solution :

1 year can be decomposed into 4 quarters

one quarter fee = $540

Fee for 4 months = 540

Fee for 1 month = 540/4

= 135

Fees for 7 months = 7(135)

= 945

So, the fee for seven months is $945.

Problem 8 :

A metal pipe 3 metre long was found to weigh 7.6kg. What would be the weight of the same kind of 7.8m long pipe?

Solution :

Weight of 3 meter pipe = 7.6 kg

Weight of 1 meter pipe = 7.6/3

Weight of 7.8 m of pipe = 7.8 x (7.6/3)

= 19.76 kg

So, the weight of 7.8 m pipe is 19.76 kg.

Problem 9 :

Reshma prepared 18kg of Burfi by mixing Khoya with sugar in the ratio of 7 : 2. How much Khoya did she use?

Solution :

Weight of sweet = 18 kg

Quantity of Khoya = 7x

Quantity of sugar = 2x

2x + 7x = 18

9x = 18

x = 18/9

x = 2

Amount of khoya = 7(2)

= 14 kg.

Problem 10 :

A line segment 56cm long is to be divided into two parts in the ratio of 2 : 5. Find the length of each part.

Solution :

Length of line segment = 56 cm

Length of two parts = 2x and 5x

2x + 5x = 56

7x = 56

x = 56/7

x = 8

Length of first part = 2(8) ==> 16 cm 

and 

length of second part = 5(8) ==> 40 cm

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