Question

One year ago, the ratio of Honey and Piyush ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Piyush now?

A. 5 years

B. 25 years

C. 10 years

D. 15 years

​

Answer 1

QUESTION :-

One year ago, the ratio of Honey and Piyush ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Piyush now?

A. 5 years

B. 25 years

C. 10 years

D. 15 years

SOLUTION :-

=> We are given that age ratio of honey : piyush = 2:3.

=> honey's age = 2x and piyush's age = 3x.

=> one year ago, their age was 2x and 3x.

=> Since, at present,

=> Honey's age = 2x + 1

=> .°. piyush's age = 3x + 1.

=> After 5 years ,

=> honey's age = (2x+1)+5=(2x + 6)

=> piyush's age = (3x+1)+5 = (3x+6)

NOW,

=> After 5 years becomes 4:5 .

=> .°. (2x + 6)/(3x+6) = 4/5

=> 5(2x +6) = 4(3x+6)

=> 10x+30 = 12x+24

=> 12x - 10x = 30 - 24

=> 2x = 6

=> x = 3 .

Since,

=> piyush's present age = (3x+1) = (3(3)+1) = 10 years.

=> Honey's present age = (2x+1) = (2(3)+ 1) = 7 years.

Answer:-

=> piyush's present age is 10 years.

=> Honey's present age is 7 years.

Answer 2

Given

The age ratio of Honey: Piyush = 2: 3

Let

Honey’s age = $2x$

Piyush’s age = $3x$

One year ago, their age was 2x and 3x.

At present,

Honey's age =$2x+1$

Piyush's age = $3x+1$

After 5 years,

Honey’s age

$= (2x + 1) + 5 \\= (2x + 6)$

Piyush's age

$= (3x + 1) + 5\\ = (3x + 6)$

After 5 years, this ratio becomes 4: 5.

Therefore,

(2x+6) / (3x+6) = 4/5

$10x + 30 = 12x + 24 \\=> x = 3$

Honey's present age = (2x + 1)

                                    = (2(3) + 1)

                                    $\boxed{\boxed{ \underline {\bold {= 7 years}}}}$

Piyush's present age = (3x + 1)

                                     = (3(3) + 1)

                                    $\boxed{\boxed{\underline{\bold{ = 10 years}}}}}$

$\boxed{\boxed{\underlined{\bold{Therefore \ the \ answer \ is \ option C \ - 10 \ years.}}}}$