Question

the sum of the present ages of A and B is 60 years.5 years hence their ages will be in the ratio 4:3.What were their ages 5 years ago? please show the working

Answer 1

A= 30 years old

B= 20 years old

Explanation:

Let the present age of A be x years old.

Since the sum of the present ages of A and B is 60 years,

present age of B= (60-x) years old

In 5 years

A= x +5

B= 60 -x +5= 65-x

Since the ratio of A:B= 4:3,

A would represent 4 units and B would represent 3 units.

Thus
`(3)/(4)`A=B

`(3)/(4)`(x+5)= 65 -x

`(3)/(4) x + (15)/(4) = 65 - x \\ (3)/(4) x + x = 65 - (15)/(4) \\ (7)/(4) x = 61.25 \\ 7x = 61.25 * 4 \\ 7x = 245 \\ x = 245 / 7 \\ x = 35`

Thus, present age of A

= x

= 35 years old

present age of B

= 60 -x

= 60 -35

= 25 years old

5 years ago

A= 35 -5= 30 years old

B= 25 -5= 20 years old

* under the section in 5 years,
`(3)/(4) A=B` because both would be equal to 3 units each. Since B is 3 units and A is 4 units, in order to make both value the same, we divide the 4 units of A by 4 then multiply by 3 to get 3 units. Thus,
`(3)/(4)` of A is equal to B.