Time and Work problems
- 1. A can do a certain job in 10 days. B is 60% more efficient than A. The number of days, it takes B to do the same piece of work is?
Options- A. 6
- B. 61/4
- C. 62/3
- D. 8 Discuss
Correct Answer: 62/3
Explanation:
1 day work of A = 1/10 = 0.1
1 day work of B = 1/10 + 60% of 1/10 = 0.1 + 0.06 = 0.16
So number of days taken by B to complete the work = 1/0.16
= 62/3
- 2. A, B and C together earn Rs. 150 per day while A and C together earn Rs. 94 and B and C together earn Rs. 76. The daily earning of C is?
Options- A. Rs. 75
- B. Rs. 56
- C. Rs. 34
- D. Rs. 20 Discuss
Correct Answer: Rs. 20
Explanation:
? B's daily earning = Rs. (150 - 94) = Rs. 56
? A's daily earning = Rs. (150 - 76) = Rs. 74
? C's daily earning = Rs. [(150 - (56 + 74)] = Rs. 20
- 3. A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together and finish it, then out of a total wages of Rs. 75, A will get?
Options- A. Rs. 30
- B. Rs. 37.50
- C. Rs. 45
- D. Rs. 50 Discuss
Correct Answer: Rs. 45
Explanation:
Since a alone can finish a work in 10 days and B alone can do it in 15 days. So if they work together then the ration of work done by A and B is = (1/10) : (1/15).
? The wages A will get = (1/10)[(1/10) + (1/15)] x 75
= Rs. 45
- 4. If factory A turns out x cars an hour and factory B turns out y cars every 2 hours, the number of cars which both factories turn out in 8 hours is?
Options- A. 8(x + y)
- B. (8x +y)/2
- C. 16(x + y)
- D. (2x + y)4 Discuss
Correct Answer: (2x + y)4
Explanation:
? Factory A turns out x cars in one hour. Factory B turns out y/2 cars in one hour.
? In one hour both the factories A and B can turn out (x + y/2) cars
? In 8 hours both factories turn out = 8( x + y/2) cars
= 4(2x + y) cars.
- 5. A is twice as good a workman as B and together they finish a piece of work in 14 days. A alone can finish the work in?
Options- A. 11 days
- B. 21 days
- C. 28 days
- D. 42 days Discuss
Correct Answer: 21 days
Explanation:
(A's 1 day's work) : (B's 1 day's work) = 2 : 1
Now, ? (A + B)'s day's work = 1/14
? A's 1 day's work = (1/14) x 2/3 = 1/21
? A alone can finish the work in 21 days.
[Dividing 1/14 in the ratio 2 : 1 ]
- 6. 14 workers can make 1400 toys in 5 days. One day after they started the work 14 more workers joined them. How many days will they take to complete the remaining work?
Options- A. 2 days
- B. 3 days
- C. 4 days
- D. 31/2 Discuss
Correct Answer: 2 days
Explanation:
? In 5 days 14 workers make = 1400 toys.
? In 1 days 14 workers make toys = 1400/5 = 280 toys.
Number of remaining toys = 1400 - 280 = 1120
and number of total workers = 14 + 14 = 28
? 14 workers make 1400 toys in 5 days.
? 28 workers make 1120 toys = (5 x 14 x 1120)/(28 x 1400) = 2 days
- 7. 24 boys can complete a work in 12 days while 16 men can complete the same work in 9 days. In How many days will 12 boys and 12 men together complete the same work?
Options- A. 6 days
- B. 8 days
- C. 7 days
- D. 10 days Discuss
Correct Answer: 8 days
Explanation:
? In 12 days the work is done by = 24 boys
? In 1 day the work is done by = 24 x 12 = 288 boys
? In 9 days the work is done by = 16 men
? 1 day work is done by = 16 x 9 = 144 men
? 144 men = 288 boys
? 1 men = 288/144 = 2 boys
? 12 men + 12 boys = 12 x 2 + 12 = 36 boys
? 24 boys complete 1 work in 12 days
? 36 boys complete 1 work in (12 x 24)/36 = 8 days
- 8. 24 men can do a work in 16 days while 36 women can do the same work in 24 days. In how many days will 8 men and 6 women together complete the same work?
Options- A. 36 days
- B. 28 days
- C. 32 days
- D. 24 days Discuss
Correct Answer: 36 days
Explanation:
In 16 days the work is done by 24 men
? In 1 day the work is done by = (24 x 16) men
In 24 days the work is done by = 36 women
? In 1 day the work is done by = (36 x 24) women
? (16 x 24) men = 36 x 24 women
? 1 man = (36 x 24)/(16 x 24)
? 8 men = [(36 x 24)/(16 x 24)] x 8 =18 women
? 8 men + 6 women = (18 + 6) = 24 women
? 36 women do 1 work in 24 days
? 24 women do 1 work in 24 x 36 / 24 = 36 days
- 9. A alone can complete a work in 12 days and B alone can complete the same work in 24 days. In how many days can A and B together complete the same work?
Options- A. 6 days
- B. 4 days
- C. 10 days
- D. 8 days Discuss
Correct Answer: 8 days
Explanation:
A's 1 day's work = 1/12
B's 1 day's work = 1/24
(A + B) 1 day's work = 1/12 + 1/24 days
= (2 + 1)/24 = 3/24 = 1/8
? (A + B)'s will finish the work in 8 days.
- 10. A can do a piece of the work in 10 days and B in 20 days. They begin together but A leaves 2 days before the completion of the work. The whole work will be done in?
Options- A. 8 days
- B. 7 2/3 days
- C. 7 days
- D. 6 days Discuss
Correct Answer: 8 days
Explanation:
Let the required days be x.
A works for (x - 2) days, while B work for x days.
According to the question
(x - 2)/10 + x/20 = 1
? 2x - 4 + x = 20
? 3x = 24
? x = 8 days
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