UPSC Prelims 2026 CSAT, question 13

Topic: Arithmetic

Q13

A toy $T$ jumps forward or backward. In each forward jump, it moves $5'$ forward whereas in each backward jump, it moves $2'$ backward. If in 31 jumps, $T$ moves exactly $15'$ forward, then what is the difference of the number of forward and backward jumps?

(a) 6
(b) 7
(c) 8
(d) 9Correct answer

Solution.

Answer: (d) 9

Let $f$ be the number of forward jumps and $b$ be the number of backward jumps, so $f + b = 31$ and $5f - 2b = 15$ .
Substituting $b = 31 - f$ gives $5f - 2(31 - f) = 15$ , so $7f = 77$ , which yields $f = 11$ and $b = 20$ .
The difference between the numbers of forward and backward jumps is $|11 - 20| = 9$ .