CAT 2015 | Question: 77

Question

In a mile race, Akshay can be given a start of $128$ m by Bhairav. If Bhairav can give Chinmay a start of $4$ m in a $100$ m dash, then who out of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (One mile is $1,600$ m.)

• A. Akshay, $1/12$ mile
• B. Chinmay, $1/32$ mile
• C. Akshay, $1/24$ mile
• D. Chinmay, $1/16$ mile

Answer 1

Let’s draw the diagram for a better understanding

DIAGRAM 1

When Braves completes $1 \text{mile} = 1600 \; m$ at that time Akshay can completes $= 1600 – 128 = 1472  \; m.$

Now, We can write like this,

• $B \longrightarrow 1600 \;  m$
• $B \longrightarrow 100 \;  m$
• $A \longrightarrow 1472 \;  m$
• $A \longrightarrow 92 \;  m$

DIAGRAM 2

• $B \longrightarrow 100 \;  m$
• $C \longrightarrow 96 \;  m$

We can conclude that,

• $A \longrightarrow 92 \;  m$
• $B \longrightarrow 100 \;  m$
• $C \longrightarrow 96 \;  m$

If Akshay and Chinmey are participating in the race, chimney should be the winner.

DIAGRAM 3

• $C \longrightarrow 96 \;  m \times 25$
• $A \longrightarrow 92 \;  m \times 25$
• $C \longrightarrow 2400 \;  m$
• $A \longrightarrow 2300 \;  m$

$\therefore$ The final lead given by the winner to the loser $= 100 \; m = \frac{100 \; m}{1600 \; m} = \frac{1}{16} \text{mile}.$

Correct Answer $: \text{D}$