# Time and Work

1. A alone can complete a piece of work in 15 days and B & C together can complete the same work in 8 1/3 days. B is 100% more efficient than C. How many days is required to complete the work if A and C work together ?
12 days
8 days
6 days
9 3/8 days
5 days
Option D
LCM of 15 and 8 1/3 days = 75
efficiency of A = 75/15 = 5
efficiency of B and C = 75 * 3/25 = 9
let efficiency of C = 100
efficiency of B = 200
ratio of efficiency of B and C = 2 : 1
efficiency of B = 9 * 2/3 = 6
efficiency of C = 9 * 1/3 = 3
time = 75/(5 + 3) = 75/8 = 9 3/8 days

2. Rajat alone can complete a piece of work in ‘x’ days and Sujit alone can complete the same work in (x + 5) days. If they together can complete the same work in 6 days, then find in how days Sujit can complete the whole work ?
10 days
6 days
8 days
5 days
15 days
Option E
1/x + 1/x + 5 = 1/6
2x + 5 / x^2 + 5x = 1/6
x^2 + 5x = 12x + 30
x^2 – 7x – 30 = 0
x = 10 , – 3
Days can not come in negative, so that value of x = 10
Days taken by Sujit to complete the work = x + 5 = 15 days

3. A alone can complete a work in 25 days and B alone can complete same work in 45 days. How many days are taken by A and B together to complete 60% of work ?
14 days
135/14 days
68/7 days
18/5 days
9 2/5 days
Option B
LCM of 25 and 45 = 225
efficiently of A = 225/ 25 = 9
efficiently B = 225/45 = 5
days = 225/14 * 60/100 = 135/14 days

4. A and B can complete a work in 24 days and B and C together can complete the same work in 30 days. A and C together work for 15 days and after 15 days A and C left the work, remaining work done by alone B. If the efficiency ratio of A and B is 2 : 3, then find in how many days total work will be completed ?
28 days
60 days
40 days
38 days
25 days
Option C
LCM of 24 and 30 = 120
total work = 120
efficiency of A and B = 120/24 = 5
efficiency of B and C = 120/30 = 4
efficiency of A = 5 * 2/5 = 2
efficiency of B = 5 – 2 = 3
efficiency of C = 4 – 3 = 1
A and C together work for 15 days = (2 + 1) * 15 = 45
remaining work = 120 – 45 = 75
days required to complete remaining work = 75/3 = 25 days
total days = 15 + 25 = 40days

5. P , Q and R together can complete a work in 20 days and the ratio of time taken by P , Q and R is 8 : 6 : 3. How many days is taken by Q and R together to complete the whole work ?
18 days
25 days
26 days
30 days
32 days
Option B
Time ratio of P , Q and R = 8 : 6 : 3
LCM of 8, 6 and 3 = 24
efficiency ratio of P, Q and R = 24/8 : 24/6 : 24/3 = 3 : 4 : 8
let efficiency of P , Q and R = 3x , 4x and 8x respectively.
total work = 20 ( 3x + 4x + 8x ) = 300x
time taken by Q and R together complete the work = 300x / 12x = 25 days

6. The efficiency of Rohit is 40% more than Suraj. If Suraj alone can do a work in 14 days, then find how many days is taken by Rohit to complete the whole work ?
10 days
15 days
22 days
13 days
18 days
Option A
Efficiency of Suraj = 5x
Efficiency of Rohit = 5x * 140/100 = 7x
total work = 14 * 5x = 70x
time taken by Rohit to complete the work = 70x/7x = 10 days

7. A and B can do a work in 10 days B and C can do the same work in 12 days and A and C can do the same work in 15 days. How many days by A, B and C together to complete total work ?
5 days
8 days
14 days
15 days
6 days
Option B
LCM of 10 , 12 and 15 = 60
efficiency of A and B = 60/10 = 6
efficiency of B and C = 60/12 = 5
efficiency of A and C = 60/15 = 4
A + B + B + C + A + C = 15
A + B + C = 7.5
time = 60/7.5 = 8 days

8. 12 men do a work in 18 days. They started work together and after 8 days, 3 more joined with them. In how many days the remaining work will be completed ?
8 days
9 days
12 days
18 days
15 days
Option A
Let the remaining work completed in ‘x’ days
12 * 18 = (12 * 8) + (15 * x)
15x = 120
x = 8 days

9. Rita , Gita and Sita can do a piece of work in 24 days , 20 days and 15 days respectively. If they got total wages of rs. 3800, then find difference between the wages got by Sita and Gita.
500
800
480
400
620
Option D
LCM of 24 , 20 and 15 = 120
total work = 120
efficiency of Rita = 120/24 = 5
efficiency of Gita = 120/20 = 6
efficiency of Rita = 120/15 = 8
difference = 3800 * 8 – 6/19 = rs.400

10. If 12 men can complete a piece of work in 20 days and 15 women can complete the same work in 24 days, then in how many days 8 men and 8 women can complete the whole work ?
15 days
18 days
17 days
12 days
24 days
Option B
12 men * 20 days = 15 women * 24 days
m/w = 3/2
total work = 12 * 3 * 20 = 720
time = 720 / (8 * 3 + 8 * 2 ) = 720/40 = 18 days

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