Dear Reader, Below are three solved questions from work and distance time chapters. Hope these help your preparation.

Question 1

Panchapakesan and his wife Swarnamalya are harvesting apples. Panchapakesan can pluck one apple in 15 minutes and Swarnamalya can pluck one apple in 12 minutes. Their daughter Rupasri takes 20 minutes to eat an apple and she eats all day. How many apples will they be able to sell to the market, if they work from 6 am to 6 p.m.?

a)24 b)30 c)36 d)42

Answer : c) 36

Solution :

Panchapakesan plucks 4 and his wife plucks 5 per hour. In one hour they can pluck 9. In Twelve hours they will pluck 108. Their daughter eats 3 per hour. Hence throughout the day she will eat —72. (While the plucking is done for 12 hours by the couple, their daughter eats for 24 hours at the rate of 3 per hour) Then balance would be 108 - 72 = 36. Hence they would be taking 36 apples to market.

Question 2

Twenty two Australians and 16 Russians can complete a piece of work in 10 days, whereas 22 British and 6 Russians can complete the same work in 12 days. In how many days will one Australian, working along with one Russian and 1 British can complete the work?

a)120 days b) 40 days c)60 days d) 30 days

Answer : a) 120 days

Solution :

Let Au denote work done by 1 Australian in 1 day.
Let Ru denote work done by 1 Russian in 1 day
Let Br denote work done by 1 British in 1 day.
As per question, 22 Australians and 16 Russians can complete work in 10 days. Therefore in one day, they will complete 1/10th of work. Putting this in equation, we get :
22 Au + 16 Ru = 1/10

Similarly : 22 Br + 6 Ru = 1/12
Adding the above two equations, 22 Au + 22 Br + 22 ru = 1/10 + 1/12 = 22/120
or Au + Br + Ru = 1/120
That is, 1 Australian , 1 British and 1 Russian can complete 1/120th of work in 1 day. Hence they can complete the entire work in 120 days.

Question 3

Prabhudeva, his wife and their son went to Express Plaza in Chennai. Prabhudeva’s wife fears walking along with the escalator. All the three got onto an escalator going up .Prabhudeva reached the top in 30 seconds taking 5 steps, but the son reached 6 seconds ahead of Prabhudeva. Prabhudeva’s wife did not take any step of her own and reached the top 6 seconds after Prabhudeva. Find out a) the number of steps taken by the son, b) the distance between the two points and c) the speed of the escalator.

a) 10, 30, 5/6 b) 12, 24, 5/6 c) 18,24,4/5 d) none of these.

Answer : a) 10, 30, 5/6

Solution :

Let E be the speed of the escalator in steps per second, S the number of steps climbed by the son and N the number of steps between the two points (start and end). Prabhadeva takes 30 second to reach the top and during this time he climbs 5 steps and the escalator moved by 30 E steps. So the total number of steps is (5 + 30 E)
Thus, N = 5 + 30 E ......(1)
Applying the same logic for the son N = S + 24E ....(2)
Since Prabhudeva’s wife does not take any steps of her own,
N = 36 E ....(3)

From (2) and (3) S = 12 E
Substitute N = 5 + 30 E in eqn 2,
5 + 30 E = S + 24 E
S = 6E + 5
Substituting S value we get,
12 E = 6E + 5
6 E = 5
E = 5/6
S = 5/6 x 12 = 10
N = 30 x 5/6 + 5 = 30