Time & Work (6)

1. P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
1. 3
2. 8
3. 12
4. 4

Explanation :-

(P+Q+R)’s one day work =1/6
Let (P & R)’s one day work = pr ———-(1)
(P & Q)’s one day work = 1/8    ———–(2)
(Q & R)’s one day work = 1/12  ———–(3)
By Adding (1), (2) & (3)
(2P + 2Q + 2R)’s 1 day work = (pr) + (1/8) + (1/12)
2(P + Q + R)’s 1 day work = (pr) + (1/8) + (1/12)
2*(1/6) = (pr) + 5/24
pr = (1/3) – (5/24)
pr = 1/8
Therefore P & R can complete the work in 8 days

2. P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in — days.
1. 7
2. 8
3. 9
4. 10

Explanation :-

P’s 1 day work = 1/24
Q’s 1 day work = 1/9
R’s 1 day work = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – (7/12) = 5/12
Time taken by P to finish the remaining work = (5/12) / (1/24) = 10 days

3. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.
1. 12
2. 14
3. 16
4. 18

Explanation :-

Wages of 1 woman for 1 day = 21600/(40×30)
Wages of 1 man for 1 day = (21600×2)/(40×30)
Wages of 1 man for 25 days = (21600×2×25)/(40×30)
Number of men = 14400/(21600×2×25)/(40×30= (144×40×30)/(216×50)144/16

4. P, Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
1. Rs.40
2. Rs.70
3. Rs.90
4. Rs.100

Explanation :-

Money earned by (P + Q + R) in 1 day = 1620/9 = Rs. 180
Money earned by (P + R) in 1 day = 600/5 = Rs. 120 —(1)
Money earned by (Q + R) in 1 day = 910/7 = Rs.130 —(2)
Lets suppose Money earned by (P + Q) in 1 day =  Rs. pq —(3)
2(P+Q+R) = 120 + 130 + pq
2(180) = 250 + pq
pq = Rs. 110
Money earned by R in 1 day = 180 – 110 =  Rs. 70

5. Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?
1. Rs.1104
2. Rs.1000
3. Rs.934
4. Rs.1210

Explanation :-

Let the cost of keeping one cow for 1 day be  Rs. c  & keeping one goat for 1 day be Rs. g
& keeping one goat for 1 day be Rs. g
Given that  1c = 5g
(20c +40g)*10 = Rs.  460
[(20*5g) + 40g ) *10 = Rs. 460
1000g + 400g = 460
g = 23/70 , therefore , c = 23/14
The cost for keeping 50 cows and 30 goats for 12 days =[(50*23/14) + (30*23/70)] * 12
=> (69+575)/7 = Rs.1104