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Each question below is followed by three statements I, II and III. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. What is the sum of the present ages of Suresh and Mahesh? Statement I: Mahesh is 7 years elder than Suresh Statement II: 6 years before the ratio of ages of Suresh and Mahesh is 4 : 5 Statement III: Mahesh’s age after 10 years is 3 times half of the present age of Suresh.

Each question below is followed by three statements I, II and III. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. What is the sum of the present ages of Suresh and Mahesh? Statement I: Mahesh is 7 years elder than Suresh Statement II: 6 years before the ratio of ages of Suresh and Mahesh is 4 : 5 Statement III: Mahesh’s age after 10 years is 3 times half of the present age of Suresh. Correct Answer If data in either statement I and II together or data in statement I and III together are sufficient to answer the question

Calculation:

From statement I

The only difference between the ages of Suresh and Mahesh is given. We cannot determine the sum of ages of Suresh and Mahesh.

So, the Statement I alone is not sufficient to answer the question.

From statement II

Let the age of Suresh and Mahesh 6 years before is 4x and 5x respectively.

Then, 5x – 4x = 7

⇒ x = 7

Present age of Mahesh = (5 × 7) + 6

⇒ 35 + 6

⇒ 41 years

Present age of Suresh = (4 × 7) + 6

⇒ 28 + 6

⇒ 34 years

Sum of the present ages of Suresh and Mahesh = 41 + 34

⇒ 75 years

So the statement I and II together is sufficient to answer the question.

From statement III

No relation between their present age is given. We cannot determine the sum of the ages of Suresh and Mahesh.

So, statement III alone is not sufficient to answer the question.

From statement I and statement III together

Let after 10 years Mahesh’s will be 3x and half of the present age of Suresh is x. Then the present age of Mahesh is (3x – 10) and the present age of Suresh is 2x.

Then, (3x – 10) – 2x = 7

⇒ 3x – 10 – 2x = 7

⇒ 3x – 2x = 10 + 7

⇒ x = 17

The present age of Mahesh = (3 × 17) – 10

⇒ 51 – 10

⇒ 41 years

The present age of Suresh = 2 × 17

⇒ 34 years

Sum of present ages of Suresh and Mahesh = 41 + 34

⇒ 75 years

So, the statement I and III together are sufficient to answer the question.

∴ If data in either statement I and II together or data in statements I and III together are sufficient to answer the question.

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