Question : A delivery boy started from his office at 10 am to deliver an article. He rode his scooter at a speed of 32 km/h. He delivered the article and waited for 15 minutes to get the payment. After the payment was made, he reached his office at 11:25 am, travelling at a speed of 24 km/h. Find the total distance travelled by the boy.
Option 1: 35 km
Option 2: 40 km
Option 3: 32 km
Option 4: 30 km
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Correct Answer: 32 km
Solution :
Given: A delivery boy started from his office at 10 am to deliver an article. He rode his scooter at a speed of 32 km/h.
He delivered the article and waited for 15 minutes = $\frac{15}{60}=\frac{1}{4}$ h to get the payment.
After the payment was made, he reached his office at 11.25 am, traveling at a speed of 24 km/h, i.e. 1 h 25 mins = $\frac{17}{12}$ h.
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
Let $x$ be the distance between the delivery location and the office.
According to the question,
$\frac{x}{32}+\frac{x}{24}+\frac{1}{4}=\frac{17}{12}$
⇒ $\frac{x}{8}\times \frac{7}{12}=\frac{7}{6}$
⇒ $x=16$ km
The total distance travelled by the boy = $2x=2\times 16=32$ km.
Hence, the correct answer is 32 km.
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