Amar can do a work in 15, and Ravi can do in 25 days and Samar in 30 days. How long they will take to do the work if they work together ?
a)11/2 days | b)13/2 days |
c)50/7 days | d)20 days |
Amount of work done by Amar = 1/15
Amount of work done by Ravi = 1/25
Amount of work done by Samar = 1/30
Total amount of work done by all = 1/15 + 1/25 + 1/30 = (10 + 6 + 5)/150 = 21/150 = 7/50
thus All take 50/7 days to finish the work
Rajat alone does a piece of work in 2 days and Rajesh does it in 6 days. In how many days will the two the two do it together ?
a)3/2 days | b)4 days |
c)2 days | d)3 days |
Amount of work done by Rajat = 1/2
Amount of work done by Rajesh = 1/6
Total amount of work done by both = 1/2 + 1/6 = 2/3
Therefore both will take 3/2 days
A can do a piece of work in 24 days. If B is 60% more efficient than A, then B can complete work in :
a)17 days | b)18 days |
c)15 days | d)12 days |
A's one day's work = 1/24
Therefore, B's one day's work = 160% of 1/24
= 160/100 * 1/24 = 1/15
Therefore, B will take 15 days to finish the work.
A, B and C working together take 30 min to address a pile of envelopes. A and B together take 40 min, A and C together take 45 min. how long would each take working alone ?
a)A : 72 min, B : 90 min, C : 120 min | b)A : 42 min, B : 90 min, C : 120 min |
c)A : 72 min, B : 90 min, C : 100 min | d)A : 72 min, B : 80 min, C : 120 min |
Here 1/A + 1/B + 1/C = 1/30 ... (i)
1/A + 1/B = 1/40 .... (ii)
and 1/A + 1/C = 1/45 .... (iii)
From (i) and (ii)
1/C = 1/30 - 1/40 = 1/120
1/A = 1/45 - 1/C = 1/45 - 1/120 = 1/72
1/B = 1/40 - 1/A = 1/40 - 1/72 = 1/90
So A alone will address in 72 min, B alone will address in 90 min, and C alone will address in 120 min.
24 men completes a given job in 40 days. The number of men required to complete the job in 32 days is :
a)32 men | b)30 men |
c)35 men | d)36 men |
Here indirect proportion so less days, more men
Let the number of required men to complete the work be x
Therefore, 32 : 40 : : 24 : x
32/40 = 24/x
=> x = (24 x 40)/32 = 30
If the work done by (x – 1)men in (x + 1) days is to the work done by (x + 2) men in (x – 1) days are in ratio 9 : 10, then x is equal to :
a)5 | b)6 |
c)8 | d)7 |
Let the work by (x - 1) men in (x + 1) day = 9z
Then work done by 1 man in one day = [9z/(x - 1) * 1/(x + 1)]
Let the work done by (x + 2) men in (x - 1) days = 10z,
Therefore, Work done by 1 man in 1 day = [10z/(x + 2)(x - 1)]
Therefore, [9z/(x - 1)(x + 1)] = [10z/(x + 2)(x - 1)]
=> 9(x + 2) = 10(x + 1)
=> x = 8
a)20 hours | b)60 hours |
c)45 hours | d)46 hours |
A group of workers engaged in plastering a wall completed ½ of the work in one day and ¼ of the remaining work the next day. If still 45 square metre of wall remained to be plastered. What was the area of the wall ?
a)300 sq. metre | b)120 sq. metre |
c)240 sq. metre | d)180 sq. metre |
Let 'a' be the area to be plastered.
Here the work completed on the first day = x/2 m^{2}
The work completed on the second day = 1/4 * x/2 = x/8
Therefore, x - x/2 - x/8 = 45
Therefore x = 120 m^{2}
Rani and Sneh working separately can finish a job in 8 and 12 hours respectively. If they work for an hour alternately, Rani beginning at 9.00 a.m. When will the job be finished ?
a)7 : 30 p.m. | b)7 : 00 p.m. |
c)6 : 30 p.m. | d)6 : 00 p.m. |
Capacity of Rani and Snehper hour = 1/8 and 1/12 respectively.
Total work done by them in 1 hour = 1/8 + 1/12 = 5/24 per hour
Therefore, full work = 1 x 48/5 = 9hours then left 1/6 of work and now its Sneh turn. Sneh will do the remaining work in 30 min.
Total time taken = 9 hour 30 min
time = 9 am + 9 hour 30 min = 18.30 hour
= 6.30 pm
2 men undertake to do a job for Rs. 1400. One can do it alone in 7 days and the other 8 days. With the assistance of a boy they finish the work in 3 days. How should the money be divided ?
a)Rs. 600, Rs. 525, Rs. 275 | b)Rs. 550, Rs. 500, Rs. 350 |
c)Rs. 650, Rs. 470, Rs. 280 | d)None of the above |
Let the boy completes the work in x days, thus according to the condition
1/7 + 1/8 + 1/x = 1/3
or 1/x = 1/3 - 1/7 - 1/8 = 11/168
so x = 168/11 days
So money is to shared in the ratio
1/7 : 1/8 : 11/168 or 24 : 21 : 11
Thus A's amount = 24/56 x 1400 = Rs. 600
B's amount = 21/56 x 1400 = Rs. 525
Boy's amount = 11/56 x 1400 = Rs. 275
An amount is sufficient to pay A’s wages for 21 days and B’s wages for 28 days. The amount is sufficient to pay wages to both for :
a)22 days | b)26 days |
c)24.5 days | d)12 days |
Let the total amount be x
Here A's one day's wage = x/21
B's one day's wage = x/28
therefore, A's and B's wages = x/21 + x/28 = x/12
Therefore, the amount is sufficient to pay 12 days wages to both
Two pipes A and B can separately fill a tank in 12 minutes and 15 minutes respectively. Both the pipes are opened together. But 4 minutes after the start pipe A is turned of. How much time it will take to fill the tank ?
a)11 minute | b)6 minute |
c)12 minute | d)8 minute |
Part of tank filled by A in a minute = 1/12
Part of tank filled by B in a minute = 1/15
Therefore, total part filled in a minute = 1/12 + 1/15 = 3/20
Therefore, part filled in 4 minutes = (4 x 3)/20 = 3/5
Now remaining part = 1 - 3/5 = 2/5
Therefore, greater part, more time
1/15 : 2/5 : : 1 : x
=> x/15 = 2/5
=> x = 6 min
If 10 persons can do a job in 20 days. Then 20 persons with the twice efficiency can do the same job in :
a)10 days | b)20 days |
c)5 days | d)15 days |
Let the number of days be x.
Here efficiency is 2 : 1
Person 20 : 10
Number of days 20 : x
therefore, x = (1 x 10 x 20)/(20 x 2) = 5 days
9 men finish one third work in 10 days. The number of additional men required for finishing the remaining work in 2 more days will be :
a)78 | b)81 |
c)55 | d)30 |
Time taken by 9 men to finish the job = 30 days
Remaining job = 1 - 1/3 = 2/3
More work left so more men required (direct proportion)
[less days, more men (indirect proportion)]
Work 1/3 : 2/3y : : 9 : x
Days 2 : 10
Therefore, x = 2/3 x 10 x 9 x 3 x 1/2 = 90 men
Thus required men = 90 - 9 = 81
a)17(1/2) minute | b)23(2/7) minute |
c)20 minute | d)15 minute |
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