The present ages of Manoj and Amit are in the ratio 2:3. After 12 years, their ages will be in the ratio 11:15. The present age of Amit is:

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32 years

48 years

40 years

35 years

answer is B.

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Detailed Solution

Concept- In the beginning, we will find the relation between the present ages of Manoj and Amit and similarly we will find out the relation between their ages after 12 years.
Step 1- Let us assume Manoj and Amit ages as ‘x’ and ‘y’ respectively.
Step 2- Ratio of their present ages is 2:3.
            i.e. x:y = 2:3
            ⇒ x/y = 2/3
            ⇒ x = 2y/3 ………………………………………………………(i)
This is the relation between their ages.
Step 3- Now, after 12 years, the ratio of their ages becomes 11:15.
            After 12 years, the age of Manoj becomes x+12.
            After 12 years, the age of Amit becomes y+12.
       ∴ x+12 : y+12 = 11:15…………………………………………..(ii)
Step 4- further, calculating the above equation (ii), we get
x+12:y+12=11:15
x+12/(y+12)=11/15
x+12=(11y+132)/15
Put x = 2y/3 from equation(i),
2y/3 + 12 = (11y + 132)/15
10y+180=11y+132
11y−10y=180−132
y=48.
∵ Amit age = y = 48
The present age of Amit is 48 years.
Hence, the correct answer is option 2) 48 years.

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