Question

Amarendra and Dharmendra are brothers. One day they start at the same time from their home for Tatanagar railway station in their respective cars. Amarendra took 25 minutes to reach the station. After reaching the station Amarendra found that Dharmendra is 2500 m away from the station. The distance of Tatanagar Station from their home is 15 km. Next day Dharmendra decided to start 7 minutes early. If they drive at the same speed as the previous day then Amarendra will reach the station:

• A. 120 seconds earlier than Dharmendra
• B. 120 seconds later than Dharmendra
• C. 300 seconds earlier than Dharmendra
• D. 300 seconds later than Dharmendra
• E. At the same time with Dharmendra

Hint:

In time–speed problems, always compare effective travel times. When one person starts early, adjust his travel time by subtracting the early start from total duration.

Answer 1

The Correct Option is B

Step 1: Amarendra’s speed.
Distance = 15 km, Time = 25 minutes.
Speed of Amarendra: \[ v_A=\frac{15}{25}=0.6 \ \text{km/min} \] Step 2: Dharmendra’s distance in same time.
When Amarendra reaches in 25 min, Dharmendra still has 2.5 km left. So Dharmendra covered $15-2.5=12.5$ km in 25 min. Speed of Dharmendra: \[ v_D=\frac{12.5}{25}=0.5 \ \text{km/min} \] Step 3: Dharmendra’s total time to cover 15 km.
\[ t_D=\frac{15}{0.5}=30 \ \text{minutes} \] Step 4: Compare times with early start.
Amarendra takes 25 min. Dharmendra takes 30 min, but if he starts 7 minutes earlier: \[ \text{Effective time}=30-7=23 \ \text{minutes} \] Thus Dharmendra reaches in 23 min (relative), Amarendra in 25 min. So Dharmendra arrives $2$ minutes earlier. Step 5: Convert into seconds.
\[ 2 \ \text{minutes}=120 \ \text{seconds} \] Therefore, Amarendra reaches the station 120 seconds later. \[ \boxed{120 \ \text{seconds later}} \]