Multiple choice

Two boys $A$ and $B$ start at the same time to ride from Delhi to Palwal, $60\ km$ away. A travels $4\ km$ an hour slower than $B$. $B$ reaches Palwal and at once turns back meeting $A\ 12\ km$ from Palwal. The rate of speed of $A$ was

  1. $4\ km/hr$
  2. $8\ km/hr$
  3. $12\ km/hr$
  4. $16\ km/hr$
  5. $20\ km/hr$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed of B be v. Speed of A is v-4. Time taken by B to reach 60 km and return 12 km (total 72 km) is 72/v. Time taken by A to reach 48 km is 48/(v-4). Equating times: 72/v = 48/(v-4). 72v - 288 = 48v. 24v = 288. v = 12. Speed of A = 12 - 4 = 8 km/hr.

AI explanation

When they meet, B has traveled 60 km to Palwal plus 12 km back, totaling 72 km. At the same time, A has traveled 60 km minus 12 km, which equals 48 km. Since they traveled for the same amount of time, the ratio of B's speed to A's speed is 72 to 48, or 3 to 2. Since A travels 4 km/hr slower than B, the difference of 1 part equals 4 km/hr, meaning A's speed of 2 parts is 8 km/hr.

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