Dear Reader, Below are three sample aptitude questions slightly tricky in nature.
Narain Karthikeyan’s friend participated in a cycling feat and he drove through the lap at the rate of 6 kmph, 12 kmph, 18 kmph and 24 kmph. What is the average speed of his friend’s cycling ?
a) 15 kmph b) 18 kmph c) 14.25 kmph d) 11.52 kmph
Answer : d) 11.52 kmph
Assume the length of the lap is 72 kmph (LCM 6,12,18 and 24)
Then his friend will take 12 hours, 6 hours, 4 hours and 3 hours respectively at the rate of 6,12,18 and 24 kmph. Total time taken 25 hours. Total distance 288 km
288/25 = 11.52 kmph
(We will get this same answer irrespective of whatever we assume the lap length. However, taking the LCM of the speeds has made the solution much easier.)
Krishnakumar bought an acid bottle quite evaporative in nature. He bought acid containing 24 litres of concentrated acid. He paid at the rate of Rs.2452 per litre since he could not get them at a cheaper price. On the first day 1/8 of the acid got evaporated. On the second day 2/3 of the balance got evaporated. He forgot to close the container and on the third day 1/7 of the balance acid got evaporated . How many litres of acid is left in the container?
a) 12 litres b)6 litres c)3 litres d) 18 litres
Answer : b) 6 litres.
In this problem rate at which the acid was bought is given only to distract the attention of the reader.
On the first day 1/8 got evaporated means for the second day balance left is 7/8.
On the second day 2/3 of the balance got evaporated means 7/8 x 2/3 = 7/12 got evaporated
Balance acid left out = 7/8 - 7/12 = 7/24
On the third day 1/7 got evaporated means what is left in the container is 6/7 of the balance at the end of second day.
Quantity of acid left in the container = 7/24 x 6/7 = 1/4
1/4 x 24 = 6 litres
Ramesh and Rahul were making joint-study for their semester examinations and the lights went off. It was around 10.00 pm . They lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When they finally went to sleep, the thick candle was thrice as long as the thin one. Approximately at what time did they go to sleep?
a) 1.00 am b) 1:24 am c) 11.00 pm d) none of these.
Answer : b) 1:24 am
Assume that the initial length of both the candle was L and they studied for X hours.
Consider thick candle :
In 6 hours the entire length would be burnt. Therefore in 1 hour L/6th of the candle would be burnt. Similarly in X hours, XL/6 th of the candle would be burnt.
Applying same logic to thin candle, length of thin candle burnt in X hours = XL/4
After X hours, total thick candle remaining = L - XL/6
After X hours, total thin candle remaining = L - XL/4
Also, it is given that the thick candle was thrice as long as the thin one when they finally went to sleep.
(L - XL/6) = 3(L - XL/4)
(6 - X)/6 =(12 - 3X)/4
24 - 4X = 72 - 18X
X = 3.4 (approximately) = 3 hours and 24 minutes (as .4 hours = 4/10 x 60 = 24 minutes)
So they slept 3 hours and 24 minutes after 10.00 p.m i.e. at 1.24 am.