Question

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 $6:5$

• A. Any two of I, Il and III
• B. I or IlI only
• C. Any one of the three
• D. All I, Il and III are required

Answer 1

The correct option is A Any two of I, Il and III

Let Ayush's present age $=x$

Let Deepak's present age $=y$

We have to find out $x-y=$ ?

Statement 1

we have $x:x+8=4:5$

$\frac{x}{x+8}$ $=$ $\frac{4}{5}$

$x=32$ years

Statement 2

$\frac{x}{y}$ $=$ $\frac{4}{3}$

$y=\frac{3x}{4}$

we get $y=\frac{3}{4}\times 32$ $=$ $24$ years

Statement 3

$\frac{y}{y-4}$$=\frac{6}{5}$

$y=24$ years.

Hence $x-y=32-24$$=8$

We can see any if we don't know any one of the three statements, we are still able to answer the question based on other two statements.

Thus the correct answer is $A$