Quantitative Aptitude Quiz for SSC (Time & Work): 15 March 2021

Source: safalta

a) 54

b) 72

c) 108

d) 96

Solution: here M1= 40, D1= 8 hrs, W1= 60, M2= 32, D2 =12 hrs, W2=?

M1D1T1/W1 = M2D2T2/W2

40×8/6= 32×12/W2; W2= 72 Days

a) 66

b) 99

c) 44

d) 88

Solution: From the above formula i.e. M1D1T1/W1 = M2D2T2/W2

So, (9*6*88/1) = (6*8*d/1); on solving, d = 99 days.

a) 4 days

b) 4.44 days

c) 6.66 days

d) 3.33 days

Solution - A's efficiency = 20%, B's efficiency = 10%. If they work together they can do 30% of the job in a day. To complete the job they need 3.33 days.

a) 15 days

b) 20 days

c) 25 days

d) 30 days

Solution - Let efficiency percentage as x

A's efficiency = 2x and B's efficiency = x

A is twice efficient and can complete the job 30 days before B. So,

A can complete the job in 30 days and B can complete the job in 60 days

A's efficiency = 1/30 = 3.33%

B's efficiency = 1/60 = 1.66%

Both can do 5% ( 3.33% + 1.66% ) of the job in 1 day.

So they can complete the whole job in 20 days (100/5)

a) 5

b) 7.5

c) 10

d) 12.5

Solution: Ratio of time taken by A & B = 160:100 = 8:5

Suppose B alone takes x days to do the job.

Then, 8:5:: 12: x= > 8x = 5*12= > x = 15/2 days.

a) 10

b) 12

c) 15

d) 7.5

Solution: Suppose A,B and C take x, x/2 and x/3 hours respectively finish the work then

1/x+2/x+3/x = ½ = > 6/x = ½ = >x = 12

So, B takes 6 hours to finish the work.

a) 27

b) 18

c) 21

d) 36

Solution: if A takes x days to do a work thenB takes 2x days to do the same work

= > 1/x+1/2x = 1/18= > 3/2x = 1/18= > x = 27 days. Hence, A alone can finish the work in 27 days

a) 3 : 1

b) 1 : 3

c) 2 : 3

d) 3 : 2

Taking equation 2 and 3 together

⇒ B + C = 3.33% and C + A = 3.33%⇒ C and 3.33% will be removed. Hence A = B

⇒ Efficiency of A = B = 5%/2 = 2.5% = 1/40⇒ Efficiency of C = 3.33% - 2.5% = 0.833% = 1/120

⇒ A can do the job in 40 days and C can do the job in 120 days he they work alone.

⇒ Ratio of number of days in which A and C can complete the job 1:3.

9. The speeds at which A and B work are in the ratio of 5 : 7. The numbers of days taken by them to finish same piece of work will be in the ratio of

a) 7 : 5 b) 5 : 7 c) 6 : 1 d) 1 : 6

Speeds at which A and B work are in the ratio of 5 : 7.

As speed means efficiency, the efficiency is inversely proportional to the time taken.

Thus, the ratio of the numbers of days taken by them will be 7 : 5

10. If 32 men can complete a piece of work in 42.5 days, then at least how many men are required to complete the same work in 106.25 days?

a) 12 b) 13 c) 11 d) 14

Applying work equivalence method:

Let the number of men required to complete the work in 16 days be x.

Now, according to the question,

X × 106.25 = 32× 42.5

x = 12.8

At least 13 men are required to complete the same work in 106.25 days

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