# IBPS Clerk 2019 | Time and Work | Maths | 04

1. A is 30% more efficient that B. How much time will they, working together take to complete a job which A alone could have done in 23 days?
[a] 20 days
[b] 17 days
[c] 15 days
[d] 13 days
[e] None of these

A is 30% more Efficient than B
if B = 100 then A = 130
then ratio of A and B's efficiency will be
130 : 100 = 13 : 10
If A can do the work in 23 days = 13 x 23
and together they will take = 13 x 23 / 23 = 13 days

2. The A and B and do a work in the ratio of 2:5 respectively. If A and B work together they can complete the work in 10 days. In how many days B will complete the work independently.
[a] 35 days
[b] 14 days
[c] 21 days
[d] 70 days
[e] None of these

Ratio of A and B = 2 : 5
They can complete in 10 days
Total work = 2 + 5 = 7 x 10 = 70 units
A can complete the work alone in = 70/2 = 35 days
B can complete the work alone in = 70/5 = 14 days

3. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B, working together, they can do it in how many days?
[a] 45 days
[b] 22.5 days
[c] 15 days
[d] 45.5 days
[e] None of these

A is thrice good as B
Ratio to do work = A : B = 3 : 1
Ratio of time = A : B = 1 : 3
Difference of time = 2 which is equal to 60 days
then Ratio of work will be = A : B = 30 : 90
LCM of work = 90 units
working together they can complete = 4 units
Days to complete work = 90/4 = 22.5 days

4. A does half as much work as B in three fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it alone.
[a] 45 days
[b] 30 days
[c] 60 days
[d] 90 days

B can do a work in 1 day
A can do 1/2 work in 3/4 day
A can do 1 work in 3/4 x 2 = 3/2
Now If B takes 1 day then A takes 3/2 days = 1 : 3/2
Solve further = B : A = 2 : 3 Efficiency
B : A = 3 : 2 Time (i.e. inverse the efficiency)
Total work = 18 days
A only can complete in = 18 x 5 / 2 = 45 days
B only can complete in = 18 x 5 / 3 = 30 days

5. Anjan is friend of Mukul and the ratio of their efficiency is 7 : 5. Working together they complete 40% work in 8 days and remaining work is completed by Anjan. If for doing work Anjan received Rs. 24000. Find the amount that Mukul will receive.
[a] 5000
[b] 4700
[c] 4500
[d] 4200
[e] None of the above

Ajan : Mukul = 7 : 5
40% of work in 8 days = 7+5 x 8 = 96 units
If 40% of a work is 96 units
then 100% of the work will be 96/40 x 100 = 240 units
Ajan gets 24000 for the work till end
Mukul work at the efficiency of 5 for 8 days = 5 x 8 = 40 units
So Ajan gets 24000 for 200 units
then Mukul will get = 24000/200 x 40 = 4800

6. Amit and Bhanu can do a piece of work in 9 and 18 days, respectively. As they were ill, they could do 45% and 90% of their efficiency, respectively. How many days will they take to complete the work together?
[a] 10 days
[b] 15 days
[c] 20 days
[d] 24 days
[e] None of these

Amit and Bhanu in 9 and 18 days respectively
If Amit works with efficiency of 45% he will take
9/45 x 100 = 20 days to complete the work
If Bhanu works with efficiency of 90% he will take
18/90 x 100 = 20 days to complete the work
Total work = 20 units (LCM)
Amit : Bhanu = 1:1 = 2 units per day
Total work = 20 / 2 = 10 days

7. Due to fever efficiency of Ramesh is reduced by 40% hence he takes 12 more days than earlier to complete. If next day he starts working with 50% of his original efficiency. Now in how many days he will complete the total work?
[a] 36 days
[b] 45 days
[c] 30 days
[d] 60 days
[e] None of these

Ramesh ill : Ramesh fit
60% : 100%
3 : 5 Efficiency
5 : 3 Time
difference is 2 which given is 12 days
then 1 will be 6 days
If Ramesh is ill (40%) he takes 30 days and If he is fit (100%) he takes 18 days

If Ramesh starts working with 50% efficiency he will take 36 days to complete the work

8. A is 20% less efficient that B. A started the work and work for x days after which B replaced A and completed the remaining work in (x-7) days. If the ratio of work done by A and B is 3 : 2. Working together they will complete the whole work in how many days?
[a] 5(7/23) days
[b] 11(1/9) days
[c] 4(7/23) days
[d] 7 days
[e] None of these

A : B
80 : 100
4 : 5
4*x /5 * (x-7) = 3/2
8x = 15x - 105
7x = 105
x = 15
4*15 = 60, 5* (15 - 7)/9
60 + 40 / 9
100/9 = 11 (1/9)

9. A and B can complete a work in half the time of C, While B and C can complete the same work in one-third time than A. If they together complete the work in 20 days. In how many days A alone can do the same work?
[a] 60 days
[b] 48 days
[c] 80 days
[d] 72 days
[e] None of these

A and B can complete in half time of C
A+B : C
1 : 2 (Time)
2 : 1 (efficiency)

B and C can complete 1/3rd time than A
B+C : A
1 : 3 (Time)
3 : 1 (efficiency)

A+B:C = 2 : 1 = 3
B+C:A = 3 : 1 = 4

A+B:C = [2 : 1 ] x 4 = 8 : 4 = 12
B+C:A = [3 : 1 ] x 3 = 9 : 3 = 12

We will get individual efficiency
A = 3
B = 5
C = 4

Now Total work = 20 days
A can do alone = 20 x 12 / 3 = 80 days
B can do alone = 20 x 12 / 5 = 48 days
C can do alone = 20 x 12 / 4 = 60 days

10.Ramu completes 30% of work in 7.5 days. Raju is 50% as efficient as Ramu, Venu is 50% as efficient as Raju. Now Raju and Venu joined with Ramu for the rest of the work then in how many days will take to complete the work? [a] 9 Days
[b] 10 Days
[c] 12 Days
[d] 15 Days
[d]None of these

Ramu takes 25 days to complete work.
Raju = 50 days Venu = 100 days
Now 70% work is left
They can complete whole work in = 1/ 1/25+1/50+1/100
100/7 days then 70% in 10 days