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

Answer:

6 years

Step-by-step explanation:

Ratio of present ages of A and B =2:5

Sum of present ages = 42 years.

Let present age A be 2x years and B be 5x years.

2x + 5x = 42

7x = 42 = x = 6 years.

Present age of A = 2x = 2 × 6 = 12 years.

Present age of B = 5x = 5 × 6 = 30 years.

After n years ,the ratio of their ages will be 1:2.

12+n/30+n = 1/2 .

2(12+n) = 30 + n

24 + 2n = 30 + n

1n = 30-24 = 6 years.

n = 6 years.

value of n = 6.

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Answer 2

Given:-

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

To find:-

• Find value of n

Solution:-

Let the present ages of A & B be 2a & 5a years respectively as they are in ratio of 2 : 5

According to Question :

⇒ 2a + 5a = 42

⇒ 7a = 42

⇒ a = 42/7

⇒ a = 6

⋆ PRESENT AGES :

⇒ Age of A = 2a = 2(6) = 12 years.

⇒ Age of B = 5a = 5(6) = 30 years.

So, after n years,

⇒ Age of A = (12 + n) years.

⇒ Age of B = (30 + n) years.

According to Question :

⇒ (12 + n) : (30 + n) = 1 : 2

⇒ 30 + n = 2(12 + n)

⇒ 30 + n = 24 + 2n

⇒ 30 - 24 = 2n - n

⇒ 6 = n

⇒ n = 6

Therefore,

Required value of n = 6 years.