Multiple choice

Study the question and the statements and decide which of the statement is/are not required to answer the question and hence can be dispensed with. What is the difference between the present ages of Ayush and Deepak? I. The ratio between Ayush's present age and his age after $8$ years is $4 : 5$. II The ratio between the present ages of Ayush and Deepak is $4: 3$. Ill. The ratio between Deepak's present age and his age four years ago is $6 : 5$

  1. Any two of I, Il and III

  2. I or IlI only

  3. Any one of the three

  4. All I, Il and III are required
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A Correct answer
Explanation

Statement I gives Ayush's age (A/(A+8) = 4/5 implies A=32). Statement II gives the ratio of Ayush to Deepak (A/D = 4/3). Statement III gives Deepak's age (D/(D-4) = 6/5 implies D=24). To find the difference (A-D), we only need A and D. We can find A from I, and D from II using A, or D from III. Any two statements are sufficient.

AI explanation

Statement I gives Ayush's age using the ratio 4:5 as 32 years. Statement II relates Ayush's age to Deepak's age, and statement III independently gives Deepak's age using the ratio 6:5 as 24 years. Since you can find the difference between their ages by combining any two of the three statements, any one of the three statements can be dispensed with.

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