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Quantitative Aptitude :: Time and Distance Problems And Answers

19. The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?
A. 552 km B. 502 km
C. 492 km D. 422 km
Answer & Explanation

Answer: Option A

Explanation:
Given that distance travelled in 1st hour = 35 km
and speed of the bus increases by 2 km after every one hour
Hence distance travelled in 2nd hour = 37 km
Hence distance travelled in 3rd hour = 39 km
..
Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term, a=35, number of terms,n = 12 and common difference, d=2.

The sequence a , (a + d), (a + 2d), (a + 3d), (a + 4d), . . . 
is called an Arithmetic Progression(AP)
where a is the first term and d is the common difference of the AP
Sum of the first n terms of an Arithmetic Progression(AP),
Sn = n/2[2a+(n−1)d]
where n = number of terms
Hence, [35+37+39+... (12 terms)]
= S12 = 122[2 × 35 +(12 − 1)2] 
= 6[70 + 22] = 6 × 92 = 552
Hence the total distance travelled = 552 km
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