SOLVING RATIO WORD PROBLEMS

Problem 1 :

Two numbers are in the ratio of 3 : 5. If 9 is substracted from each, the ratio becomes 12 : 23. Find the greater number?

Solution :

Let the numbers be 3x : 5x

9 is substracted from 3x and 5x.

(3x – 9)/(5x – 9) = 12/23

Doing cross multiplication. We get

23(3x – 9) = 12(5x – 9)

69x – 207 = 60x – 108

By combining the like terms

69x – 60x = 207 – 108

9x = 99

x = 99/9

x = 11

So, the greater number is 5x = 5(11) = 55.

Problem 2 :

When 7 is added to the numerator and denominator of the fraction, then the new ratio of becomes 13 : 19, what is the original ratio?

Solution :

Let x/y be the required fraction.

7 is added to the numerator and denominator of the fraction.

(x + 7) /(y + 7) = 13/19

19(x + 7) = 13(y +7)

19x + 133 = 13y + 91

So, the original ratio cannot be determined.

Problem 3 :

The ratio of age of krish and her mother is 5 : 12 and difference of their ages is 21. What will be the ratio of their ages after 3 years?

Solution :

Let 5x be krish's age and 12x be her mother's age.

Difference of their ages = 21

12x - 5x = 21

7x = 21

x = 21/7

x = 3

Age of krish = 5x = 5(3) = 15

Mother age = 12x = 12(3) = 36

After 3 years, Krish's age = 15 + 3 ==> 18

After 3 years, Mother's age = 36 + 3 ==> 39

So, the ratio is 18 : 39.

HCF of (18 : 39) is 3.

Dividing both parts by 3.

= 6 : 13

So, the ratio of their ages after 3 years = 6 : 13.

Problem 4 :

Ratio of A and B in the ratio of 5 : 8. After 6 years, the ratio of ages of  A and B will be in the ratio of 17 : 26. Find the present age of B.

Solution :

A and B in the ratio of 5 : 8.

Those two quantities will be 5x and 8x.

After 6 years the ratio of ages of A and B = 17 : 26

17/26 = (5x + 6)/(8x + 6)

By using cross multiplication. We get

17(8x + 6) = 26 (5x + 6)

136x + 102 = 130x + 156

By combining like terms

136x – 130x = 156 – 102

6x = 54

x = 54/6

x = 9

So, the present age of B = 8x = 8(9)

= 72 years

Problem 5 :

The ratio of the length of a vertical pole and its shadow on the ground is 7 : 2. Find the length of the pole, if the length of the shadow is 2.4 m.

Solution :

Let x be the length of the pole.

Given the length of the shadow is 2.4 m.

The length of

vertical pole and shadow = 7 : 2

x/(2.4) = 7/2

By using cross multiplication. We get

2x = 16.8

x = 16.8/2

x = 8.4 m

So, the length of the pole is 8.4 m.

Problem 6 :

If the cost of 14 m cloth is $1890, find the cost of 6 m cloth.

Solution :

Cost of 14 m cloth = 1890

Let x be the cost of 6 m cloth.

Ratio between quantity of cloth to its price = 14 : 1890

14 : 1890 = 6 : x

14/1890 = 6/x

14x = 6(1890)

x = 6(1890)/14

x = 810

So, cost of 6 m cloth is $810.

Problem 7 :

The value of m, if 3, 18, m, 42 are in proportion is 

a)  6     b)  54     c)  7    d) none

Solution :

3, 18, m, 42

3 : 18 = m : 42

3/18 = m/42

3(42) = m(18)

m = 3(42) / 18

m = 7

So, option c is correct.

Problem 8 :

If 20% of x = 30% of y, then x : y = ?

Solution :

20% of x = 30% of y

0.20x = 0.30y

x / y = 0.30 / 0.20

x / y = 3/2

x : y = 3 : 2

So, the required ratio is 3 : 2.

Problem 9 :

Two numbers are in the ratio fo 8 : 3 and their sum is 242. Find the difference between two numbers.

Solution :

Let the numbers be 8x and 3x.

8x + 3x = 242

11x = 242

x = 242/11

x = 22

Applying the value of x, we get

8(11) ==> 88

3(11) ==> 33

Their difference = 88 - 33

= 55

Problem 10 :

Present age of Rani and Kami are in the ratio of 5 : 6 respectively. 7 years hence this ratio will become 6 : 7 respectively. What is Rani's present age ?

Solution :

Ratio between the present age = 5 : 6

After 7 years. The new ages will be 5x + 7 and 6x + 7

5x + 7 : 6x + 7 = 6 : 7

7(5x + 7) = 6(6x +7)

35x + 49 = 36x + 42

36x - 35x = 49 - 42

x = 7

Rani's present age = 5(7) ==> 35 years