Question

the present ages of A and B are in the ratio 5:6.three years ago,their ages were in ratio 4:5. find the numbers.

Answer 1

✬ A = 15 ✬

✬ B = 18 ✬

Step-by-step explanation:

Given:

• Present ages of A and B are in ratio of 5 :6.
• Three years ago their ages were in ratio 4 : 5.

To Find:

• What are their ages ?

Solution: Let x be the common in given ratios. Therefore

➟ A's age = 5x years

➟ B's age = 6x years

[ Now, three years ago their ages were ]

➟ A's age = (5x – 3) years

➟ B's age = (6x – 3) years

A/q

• Three years ago their ages were in ratio 4 : 5.

$\implies{\rm }$ (5x – 3) : (6x – 3) = 4 : 5

$\implies{\rm }$ (5x – 3)/(6x – 3) = 4/5

$\implies{\rm }$ 5(5x – 3) = 4(6x – 3)

$\implies{\rm }$ 25x – 15 = 24x – 12

$\implies{\rm }$ 25x – 24x = – 12 + 15

$\implies{\rm }$ x = 3

So, present ages of

➨ A = 5x = 5(3) = 15 years

➨ B = 6x = 6(3) = 18 years

Answer 2

Given ,

• The present ages of A and B are in the ratio 5 : 6

• Three years ago , their ages were in ratio 4 : 5

Let , the present ages of A and B be 5x and 6x

According to the question ,

(3 - 5x)/(3 - 6x) = 4/5

15 - 25x = 12 - 24x

-25 + 24x = 12 - 15

-x = -3

x = 3

$\therefore$ The present age of A and B are 15 years and 18 years