A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. In how many days can A alone do it?
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Solution
(A + B)’s one day’s work =
(B + C)'s one day's work =
(A + C)’s one day’s work =
∴ 2(A+B+C) =
∴ (A+B+C)'s One day's work =
So, all together can finish the work in 10 days
∴ A's one day's work =
∴ A Can complete the work in 30 days.
P and Q working separately can do a piece of work in and 18 days respectively. If they work for a day alternately. Suppose P beginning the work in how many days the work will be completed?
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Solution
P’s and Q’s one day’s work =
Work done in 7 pairs of days =
Remaining work =
Required number of days =
= days.
‘X’ completes a job in 3 days and ‘Y’ completes it in 4 days and ‘Z’ takes 5 days to complete it. If they work together and get Rs. 9400 for the job then how much amount does ‘Y’ get?
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Solution
Ratio of work done by X, Y and Z =
Now, ratio in their amount = 20 : 15 : 12
∴ Part of Y = = Rs. 3000
A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
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Solution
1 minute’s work of both the punctures = =
So, both the punctures will make the tyre flat in mini.
P and Q can do a piece of work in 24 days; Q and R in 32 days, R and P in 48 days. In how many days can they do it all working together?
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Solution
(P + Q)’s one day’s work =
(Q + R)’s one day’s work =
(R +P)’s one day’s work =
∴ 2 (P + Q + R) =
⇒ P + Q + R =
∴ Required number of days = days.
Anil and Suresh are working on a special assignment. Anil needs 8 hours to type 36 pages on a computer and Suresh needs 9 hours to type 72 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 180 pages?
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Solution
Pages typed by Anil in 1 hour =
Pages typed by Suresh in 1 hour =
Pages typed by Anil and Suresh in 1 hour =
Time taken == 14 hour 24 minutes
P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in days if work together. How much time will Q take to do the work alone?
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Solution
Let P takes x days to complete the work
Then Q takes days and R takes days to finish the work
Amount of work P does in 1 day =
Amount of work Q does in 1 day =
Amount of work R does in 1 day =
Amount of work P,Q and R do in 1 day = + + =
=
⇒
⇒ Q takes days = 7.5 days to complete the work
If daily wages of a man is double to that of a woman, how many men should work for 50 days to earn Rs. 28800? Given that wages for 60 women for 45 days are Rs. 32400.
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Solution
Wages of 1 woman for 1 day = Rs.
Wages of 1 man for 1 day = 12 × 2 = Rs. 24
Wages of 1 man for 50 days = 24 × 50 = Rs. 1200
Number of men =
Amit, Bipin and Chandan together earn Rs. 3240 in 18 days. Amit and Chandan can earn Rs. 1200 in 10 days. Bipin and Chandan in 14 days can earn Rs. 1820. How much amount does Chandan can earn per day ?
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Solution
Amount Earned by Amit, Bipin and Chandan in 1 day = ---(1)
Amount Earned by Amit and Chandan in 1 day = = 120 ---(2)
Amount Earned by Bipin and Chandan in 1 day = = 130 ---(3)
Equation (2) + (3) – (1)= 120 + 130 – 180 = 70
⇒ Amount Earned by Chandan in 1 day = Rs. 70
30 cows and 60 goats can be kept for 15 days for Rs. 840. If the cost of keeping 6 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 75 cows and 45 goats for 18 days?
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Solution
Assume that cost of keeping a cow for 1 day = c ,
cost of keeping a goat for 1 day = g
Cost of keeping 30 cows and 60 goats for 15 days = 840
Cost of keeping 30 cows and 60 goats for 1 day = 840/15 = 56
⇒ 30c + 60g = 56
⇒ 15c + 30g = 28 ---(1)
Given that 6g = c
Hence equation (1) can be written as 15c + 5c = 28 ⇒ 20c =28
⇒ c = 28/20
cost of keeping 75 cows and 45 goats for 1 day
= 75c + 45g
= 75c + 45/6c (substituted 6g = c)
= 82.5 c = 82.5×28/20
= 115.5
Cost of keeping 75 cows and 45 goats for 18 days = 18×115.5 = 2079