A and B runs a Km race. If A gives B a start of 50 m, A wins by 14 sec and, if A gives B a start of 22 sec Km, B wins by 20 m. The time taken by A to run a Km is:

Let, times (in sec) taken by A and B to run a Km, be P and Q, respectively.
When B gets a start of 50 m, B runs.
1000 - 50 = 950 m while A runs 1000 m.
∴ 950 / 100 Q - P = 14,
i.e., 0.95Q - P = 14 …(1)
and, when B gets a start of 22 seconds, A runs for (Q - 22) seconds, while B runs for Q seconds.
∴ 1000 - 1000 / P (Q - 22) = 20
i.e., 50Q - 49P = 1100. …(2)
Multiplying Eq. (1) by 49 and subtract from Eq. (2)
3.45Q = 414
∴ Q= 120 sec.
∴ from (1)
⇒ P = 0.95 × 120 - 14 = 100 seconds.