1. 40 people can make 60 toys in 8 hrs, if 8 people leave the work, then how many toys can be made in 12 hrs?
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
2. If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do the same work in how many days?
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.
3. A take 5 days to complete a job and B takes 10 days to complete the same job. In how much time they will complete the job together?
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.
4. A is twice as efficient as B and can complete a job 30 days before B. In how much they can complete the job together?
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)
5. A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B alone take to do the same job?
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.
6. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together they can finish the work in 2 days. B can do the work alone in how any days?
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.
7. A is twice as good a workman as B and together they finish a piece of work in 18 days.In how many days will A alone finish the work.
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
8. - A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 30 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?
a) 3 : 1
b) 1 : 3
c) 2 : 3
d) 3 : 2
Solution - ⇒ Efficiency of A and B = 1/20 per day = 5% per day, Efficiency of B and C = 1/30 per day = 3.33% per day, Efficiency of C and A = 1/30 per day = 3.33% per day
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