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.