Question

In a row of $40$ boys, Satish was shifted $10$ places to the right of Rohan and Kartik was shifted $10$ places to the left of Vikas. If Vikas was twenty-sixth from the left and there were three boys between Kartik and Satish after shifting, what was the position of, Rohan in the row?

• A. ${10}^{th}$ from the right end
• B. ${10}^{th}$ from the left end
• C. ${39}^{th}$ from the right end
• D. Data inadequate

Answer 1

The correct option is D Data inadequate

The answer is option $D$

Let's number the position from the left

$\Rightarrow$ The first position from left $=1$ and so on.

$\Rightarrow$ Moving towards the right will increase the count and moving toward left will decrease the count

Satish was shifted 10 places to the right of Rohan

$\Rightarrow S=R+10\to \left(I\right)$

Karthik was shifted 10 places to the left of Vikas

$\Rightarrow K=V-10\to \left(II\right)$

Vikas was twenty-sixth from left

$\Rightarrow V=26$

$\Rightarrow K=V-10=16$

There were $3$ boys between Karthik and Satish after shifting

$\Rightarrow$ Difference between Karthik and Satish $=4$

$\Rightarrow$ Either $K-S=4$ or $S-K-4$

$\text{Case 1:}$ $K-S=4$

$\Rightarrow S=K-4=16-4=12$

$\Rightarrow R=S-10$ (from $\left(I\right)$)=12-10=2

$\Rightarrow$ Rohan is $2^{nd}$ from left

$\text{Case 2:}$ $S-K=4$

$\Rightarrow S=K+4=16+4=20$

$\Rightarrow R=S-10$ (from $\left(I\right)$)=20-10=10

$\Rightarrow$ Rohan is ${10}^{th}$ from left

Since both cases can be true, we cannot say for sure the correct answer without additional data. Hence data is inadequate to answer this question.