Test Level 1: Time & Work - 2 - CAT MCQ

Work done by Q

Assume each man could do 'x' work in 1 day.
So, total work = 10 × 40x = 400x
But they completed the work in 34 days (40 - 6).
Assume after 'd' days, they increased their efficiency.
After increasing the efficiency, they could do 1.25x work in 1 day.
So, 400x = 10 × d × x + 10 (34 - d)1.25x.
⇒ 40 = d + (34 - d)1.25
⇒ 0.25d = 2.5  d = 10
Thus, they increased their efficiency 10 days after the start of the work.
Hence, answer option 4 is correct.

Suppose the first pipe takes A minutes, the second pipe takes B minutes, the third pipe takes C minutes and the fourth pipe takes D minutes to fill the pool.

Add equations (ii), (iii) and (iv): 

The fifth pipe can empty the tank in 30 minutes.
So, combined time taken by all the five pipes

He will complete the work in 20 days. Hence, he will complete ten times the work in 200 days.

A’s one day work will be 5%, while B will do 6.66 % of the work in one day. Hence, their total work will be 11.66% in a day.
In 8 days they will complete → 11.66 x 8 = 93.33%
This will leave 6.66% of the work. This will correspond to 4/7 of the ninth day since in 6.66/11.66 both the numerator and the denominator are divisible by 1.66.

N + A = 10% 
N = 8.33% 
Hence A = 1.66% → 60 days.

24 man days + 18 women days = 20 man days + 28 woman days
→ 4 man days = 10 woman days.
→ 1 man day = 2.5 woman days
Total work = 24 man days + 18 woman days = 60 woman days + 18 woman days = 78 woman days.
Hence, 1 man + 1 woman = 3.5 women can do it in 78/3.5 = 156/7 = 22(2/7) days.

A = 10%, B = 5% and Combined work is 20%. Hence, C’s work is 5% and will require 20 days.

A = 20%, B = 10% and A + B + C = 50%. Hence, C = 20%. Thus, in two days, C contributes 40% of the total work and should be paid 40% of the total amount.

Let the time taken by Arun be ‘t’ days. Then, time taken by Vinay = 2t days. 1/t + 1/2t = 1/7 → t = 10.5

30X = 20 (X + 6) → 10X = 120 → X = 12.

Raju = 10%, Vicky = 8.33% and Tinku = 6.66%. Hence, total work for a day if all three work = 25%.
In 2 days they will complete, 50% work. On the third day onwards Raju doesn’t work. The rate of work will become 15%. Also, since Vicky leaves 3 days before the actual completion of the work, Tinku works alone for the last 3 days (and must have done the last 6.66 x 3 = 20% work alone). This would mean that Vicky leaves after 80% work is done. Thus, Vicky and Tinku must be doing 30% work together over two days.
Hence, total time required = 2 days (all three) + 2 

Let Anjay take 3t days, Vijay take 2t days and Manoj take 6t days in order to complete the work. Then we get: 1/3t +
1/2t + 1/6t = 1 → t = 1. Thus, Manoj would take 6t = 6 days to complete the work.

Since the ratio of money given to Apurva and Amit is 2:3, their work done would also be in the same ratio. Thus, their time ratio would be 3:2 (inverse of 2:3). So, if Apurva takes 12 days, Amit would take 8 days and the total number of days required (t) would be given by the equation:
(1/12 + 1/8)t = 1 → t = 24/5 = 4.8 days

40n = 30 (n + 5) → n = 15

A’s rate of working is 10 per cent per day while B’s rate of working is 5 per cent per day. In 5 days they will complete 75 per cent work. Thus the last 25 per cent would be done by B alone. Working at the rate of 5 per cent per day, B would do the work in 5 days.

Ajay’s daily work = 4.1666%, Vijay’s daily work = 3.33% and the daily work of all the three together is 8.33%. Hence, Pradeep’s daily work will be 0.8333%. Hence, he will end up doing 10% of the total work in 12 days. This will mean that he will be paid ₹ 20.

A + V + S = 1      (1) 
A + V = 19/23 
V + S = 8/23 
→ A + 2V + S = 27/23     (2) 
(2)–(1) gives us: V = 4/23.

After 27 days, food left = 4 x 200 = 800 soldier days worth of food. Since, now there are only 80 soldiers, this food would last for 800/80 = 10 days.
Number of extra days for which the food lasts = 10 – 4 = 6 days.

Ajay + Vijay = 1/28 and Ajay + Vijay + Manoj = 1/21.
Hence, Manoj = 1/21 – 1/28 = 1/84.
Hence, Manoj will take 84 days to do the work.