Ratio of the present ages of Abhik and Anuja is 3 : 2. After 15 years

1.	Ratio of the present ages of Abhik and Anuja is 3 : 2. After 15 years ratio of ages of Abhik and Ankan will be 9 : 5 and that between Anuja and Ankan will be 7 : 5. What is the present age of Ankan?1. 25 years2. 20 years3. 10 years4. 15 years5. Can’t be determined
Answer» Correct Answer - Option 3 : 10 years Given: Ratio of the present ages of Abhik and Anuja is 3 : 2. After 15 years ratio of ages of Abhik and Ankan will be 9 : 5. After 15 years ratio of ages of Anuja and Ankan will be 7 : 5 Calculation: Let us assume present ages of Abhik, Anuja and Ankan be 3x, 2x and y respectively. ATQ, \(\frac{{3x\; + \;15}}{{y\; + \;15}} = \;\frac{9}{5}\) ⇒ 15x + 75 = 9y + 135 ⇒ 15x – 9y = 60 ----(1) And, \(\frac{{2x\; + \;15}}{{y\; + \;15}} = \;\frac{7}{5}\) ⇒ 10x + 75 = 7y + 105 ⇒ 10x – 7y = 30 ----(2) Solving (1) & (2), y = 10 Present age of Ankan = 10 years.

Ratio of the present ages of Abhik and Anuja is 3 : 2. After 15 years ratio of ages of Abhik and Ankan will be 9 : 5 and that between Anuja and Ankan will be 7 : 5. What is the present age of Ankan?1. 25 years2. 20 years3. 10 years4. 15 years5. Can’t be determined

Answer» Correct Answer - Option 3 : 10 years

Given:

Ratio of the present ages of Abhik and Anuja is 3 : 2.

After 15 years ratio of ages of Abhik and Ankan will be 9 : 5.

After 15 years ratio of ages of Anuja and Ankan will be 7 : 5

Calculation:

Let us assume present ages of Abhik, Anuja and Ankan be 3x, 2x and y respectively.

ATQ,

\(\frac{{3x\; + \;15}}{{y\; + \;15}} = \;\frac{9}{5}\)

⇒ 15x + 75 = 9y + 135

⇒ 15x – 9y = 60 ----(1)

And,

\(\frac{{2x\; + \;15}}{{y\; + \;15}} = \;\frac{7}{5}\)

⇒ 10x + 75 = 7y + 105

⇒ 10x – 7y = 30 ----(2)

Solving (1) & (2), y = 10

Present age of Ankan = 10 years.

Discussion

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