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Quantitative Aptitude Quiz for UPSI (Time and Work): 16 April 2021

Updated Fri, 16 Apr 2021 09:31 PM IST
Source: safalta
 
1. Rose and Merry can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days Merry had to leave and Rose alone completed the remaining work. The whole work was completed in?

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a) 10 days
b) 15 days
c) 12 days
 
d) 8 days
 
(R+M)’s 1 day’s work = (1/15 + 1/10 ) = 1/6
 
Work done by R and M in 2 days = 1/6 × 2 = 1/3
Remaining work = 2/3
Now, work will be done by R in 1 day work will be done by R in ( 15 x 2/3)  = 10
Hence, total time taken = (10+2) = 12 days
 
2. Amit can finish a work in 24 days, Bunty in 9 days and Cathy in 12 days. Bunty and Cathy start the work but are forced to leave after 3 days. The remaining work was done by Amit in?
a) 6 days
b) 5 days
c) 10 days
d) 10.5days
 
(B+C)’s 1 day’s work = ( 1/9 + 1/12) = 7/36
 Work done by B and C in 3 days = 7/12
Remaining work = 5/12
Now 1/24 work is done by A in 1 day So,
5/12 work is done by A in 10 days
 
3. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days .Y joined him till the completion of the work. How long did the work last?
a) 6 days
 
b) 10 days
 
c) 15 days
 
d) 20 days
 
Work done by X in 4 days = 1/20 x 4 = 1/5
Remaining work = 4/5
(X+Y)’s 1 day’s work = ( 1/20 + 1/12 ) = 2/15
 Now, 2/15 work is done in X and Y in 1 day
So, 4/5 work will be done by X and Y in (15/2 x 4/5 ) = 6 days
Hence, total time taken = (6+4) days = 10 days
 
4. Adam and Bob can together finish work in 30 days .They worked together for 20 days and then Bob left. After another 20 days, Adam finished the remaining work .In how many days Adam alone can finish the job?
a) 40
b) 50
c) 54
d) 60
(A+B)’s 20 day’s work = (1/30 x 20 = 2/3 )
Remaining Work = 1/3
Now, 1/3 work is done by A in 20 days
Whole work will be done by A in 60 days
 
5. A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leave off The total number of days to complete the work is?
a) 6 3/5
b) 8 1/2
c) 10 1/5
d) 13 ½
B’s 3 day’s work = (1/21 x 3 = 1/7 )
 Remaining work = ( 1 – 1/7 ) = 6/7
(A+B)’s 1 day’s work = ( ) Now, 5/42 work is done by A and B in 1 day
work is done by A and B in ( 42/5 x 6/7 ) = 36/5 days
Total time taken= 3 + 36/5 = 51/5

6. Andy, Ben and Cherrie together earn Rs.300 per day, while Andy and Cherrie together earn Rs.188 and Ben and Cherrie together earn Rs.152.The daily earning of Cherrie is?
a) Rs.40
 
b) Rs.112
 
c) Rs.68
 
d) Rs.150
 
Option A
B’s daily earning = Rs. (300 – 188) = Rs. 112
A’s daily earning = Rs. (300 – 152) = Rs. 148.
C’s daily earning = Rs. [30 – (112 + 148)] = Rs 40
 
7. A,B and c are employed to do a piece of work for Rs.529.A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. What amount should A be paid?
a) Rs.315
 
b) Rs.345
 
c) Rs.375
 
d) Rs.355
 
Work done by A = ( 1 – 8/23) = 15/23
 A: (B+C) = 15/23 : 8/23 = 15:8
So, A’s share = Rs (15/23 x 529 ) = Rs 345
 
 
 
8. A sum of money is sufficient to pay A’s wages for 21 days and B’s wages for 28 days. The same money is sufficient to pay the wages of both for?
a) 12 days
 
b) 14 days
 
c) 121/4 days
 
d) 24 ½ days
 
Let total money be Rs. X
A’s 1 days’ wage = x/21,
B’s 1 day’s wage = x/28
 Rs (A+B)’s 1 day’s wage = Rs(x/21 + x/28 ) = x/28
 Money is sufficient to pay the wages of both for 12 days
 
9. A water tap fills a tub in ‘p’ hours and a sink at the bottom empties it in ‘q’ hours. If ‘p < q and both tap and sink are opened the tank is filled in ‘r’ hours; then the relation between p, q, r is:
 
(a)1/r=1/p+1/q
(b)1/r=1/p-1/q
(c)r=p+q
(d)r=p–q
 
Sol
1/r=1/p-1/q
 
10. A water reservoir has two inlets and one outlet. Through the inlet it can be filled in 3 hours and 3 hours 45 minutes respectively. It can be emptied completely in 1 hour by the outlet. If the two inlets are opened at 01:00 pm and 02:00 pm respectively and the outlet at 03:00 pm then it will be emptied at:
 
(a)05:55pm
(b)05:00pm
(c)05:20pm
(d)05:30pm



                                                Total work                           Efficiency
1st Inlet   3                                                                           5
2nd Inlet  15/4                     15                                           4
3rd Inlet    - 1                                                                       -15
 
Work done by two inlet pipes upto 3 pm = 5 + 4 + 5= 14Efficiency of All the pipes = 5 + 4 – 15= –6
In two hours work done by All the pipes = –6 × 2= –12
Remaining work = 14 – 12= 2
2 work will be done by all the pipe in= 2/6= 1/3 hours= 20 minutes
Time at which the tank will be empty
= 3:00 + 2h + 20 minutes
= 5 : 20 pm
 

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