Question

The ratio of the present ages of A and B is 2 : 5. After n years, the ratio of their ages will be 1 : 2 . If the sum of their present ages is 42 years, then find the value of n.

Answer 1

Given:-

• Present age ratio = 2 : 5
• After n years, ratio will be 1 : 2
• Sum of present ages = 42 years.

To find:-

• Value of n = ?

Solution:-

Let the present ages of A & B be 2y & 5y years respectively.

A/q,

→ 2y + 5y = 42

→ 7y = 42

→ y = 42/7

→ y = 6 ------- Equation (1)

Case 2 :

→ (2y + n) : (5y + n) = 1 : 2

→ (2y + n)/(5y + n) = 1/2

→ 5y + n = 2(2y + n)

→ 5y + n = 4y + 2n

→ 5y - 4y = 2n - n

→ y = n ------- Equation (2)

Comparing both equations :-

→ n = 6 years.

Therefore,

Required value of n = 6

Answer 2

Question-

The ratio of the present ages of A and B is 2 : 5. After n years, the ratio of their ages will be 1 : 2 . If the sum of their present ages is 42 years, then find the value of n.

_________________________

Given-

Ratio of present age = 2:5

After n years, ratio = 1:2

Sum of present ages = 42 years

_________________________

To find -

Value of n

_________________________

Solution-

Let the ages of A and B be 2x and 5x

Then,

➠2x + 5x = 42 years

➠7x = 42

➠x = 42/7

➠x = 6____________(eq.1)

_________________________

➠(2x + n) : (5x + n) = 1 : 2

➠(2x + n )/(5x + n) = 1/2

➠5x + n = 2(2x + n)

➠5x + n = 4x + 2n

➠5x - 4x = 2n - n

➠x= n ________(eq.2)

_________________________

By the equations,

n = x,

x=6

➠n = 6 years

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