Time and Work problems
- 1. If 12 man or 18 women can do piece of work in 14 days. How long will 8 men and 16 women take to finish the work?
Options- A. 9 days
- B. 12 days
- C. 13 days
- D. 10 days Discuss
Correct Answer: 9 days
Explanation:
12 men =18 women
? 1 man = 18/12 women
? 8 men = 18/12 x 8 = 12 women
Given m1 = 18 M2 = 12 +16 = 28,
D1 , D2 = ? and W1 = W2 = 1
According to the formula
M1D1W2 = M2D2W1
? 18 x14 x1= 28 x D2 x1
? D2 = (18 x 14)/28 = 9 days
- 2. 10 man can make a wall in 8 days. How many men required to complete the same work in half days?
Options- A. 80
- B. 100
- C. 120
- D. 160 Discuss
Correct Answer: 160
Explanation:
Given, M1 = 10 D1 = 8, M2 = ? and D2 = 1/2
From M1D1 = M2D2
? 10 x 8 = M2 x 1/2
? M2 = 10 x 8 x 2
? M2 = 160
- 3. 6 boys can complete a piece of work in 16 h. In how many hours will 8 boys complete the same work?
Options- A. 10
- B. 8
- C. 12
- D. 14 Discuss
Correct Answer: 12
Explanation:
Given, M1 = 6, M2 = 8 , T1 = 16 h,
and T2 = ?, W1 = W2 = 1
According to the formula.
M1T1W2 = M2T2W1
? 6 x 16 x 1 = 8 x T2 x 1
? T2 = 16 x 6/8 = 2 x 6 = 12 h
- 4. In a hostel, there are 120 students and food stock is for 45 days. If 30 new students join the hostel, in how many days will the complete stock be exhausted?
Options- A. 38
- B. 40
- C. 32
- D. 36 Discuss
Correct Answer: 36
Explanation:
Let food stock will be exhausted in x days .
Given, m1 = 120, D1 = 45
M2 = 120 + 30 = 150
and D2 = ?
Then, using M1D1 = M2D2
? 120 x 45 = 150 x D2
? D2 = 120 x 45/120 = 36
- 5. If 5 days take 7 h to pack 35 toys, how many boys can pack 65 toys in 3 h?
Options- A. 26
- B. 39
- C. 45
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Given, M1 = 5, M2 = ?, T1 = 7, T2 = 3,
W1 = 35 and W2 = 65
According to the formula,
M1T1W2 = M2T2W1
? 5 x 7 x 65= M2 x 3 x 35
? M2 = (5 x 7 x 65)/(35 x 3) = 65/3 boys
- 6. A stock of food is enough for 240 men for 48 days. How long will the same stock last for 160 men?
Options- A. 54 days
- B. 60 days
- C. 64 days
- D. 72 days Discuss
Correct Answer: 72 days
Explanation:
M1 = 240, D1 = 48, M2 = 160 and D2 = ?
According to the formula,
M1D1 = M2D2
? 240 x 48 = 160 x D2
? D2= (240 x 48)/160 = 72
- 7. A can do a piece of work in 4 days and B can complete the same work in 12 days. What is the number of days required to do the same work together?
Options- A. 2 days
- B. 3 days
- C. 4 days
- D. 5 days Discuss
Correct Answer: 3 days
Explanation:
A 's 1 day's work = 1/4
B ' s 1 days's work = 1/12
(A+B) ' s day ' s work = 1/4 + 1/12
= (3 + 1)/12 = 4/12 = 1/3
Days required by A and B together to do the work = 1 / (A + B ) ' s day ' s work = 3 days
- 8. A , B and C can complete a work in 2 h. If A does the job alone in 6 h and B in 5 h, how long will it take for C to finish the job alone?
Options- A. 51/2 h
- B. 71/2 h
- C. 9 h
- D. 41/2 h Discuss
Correct Answer: 71/2 h
Explanation:
Let C alone can finish the job in T hours.
According to the question,
Work done by A, B and C in 1h = 1/2
? 1/6 +1/5 + 1/T = 1/2
? 1/T = 1/2 - 1/6- 1/5 = (15 - 5- 6)/30
? 1/T = 4/30 = 2/15
? T = 71/2 h
- 9. A can copy 75 pages in 25 hours. A and B together can copy 135 pages in 27 hours. In what time can B copy 42 pages?
Options- A. 21 hours
- B. 5 hours, 36 second
- C. 18 hours
- D. 24 hours Discuss
Correct Answer: 21 hours
Explanation:
In 25 hours A can copy 75 pages
In 1 hour A can copy 75/25 = 3 pages
In 25 hours (A and B) can copy = 135/27 = 5 pages
? In 1 hour B can copy (5 - 3) = 2 pages
? B can copy 42 pages in 21 hours.
- 10. Mohan can move his lawn in x hours after 2 hour it begins to rain. The unmoved part of the lawn is?
Options- A. 2/x
- B. (2 - x)/2
- C. x/2
- D. (x - 2)/x Discuss
Correct Answer: (x - 2)/x
Explanation:
? Mohan moves the whole lawn in x hours.
? mohan moves in 2 hours = 2/x part of the lawn.
? Unmoved part = 1 - 2/x = (x - 2)/ x part
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