Time and Work
- Twenty women together can complete a work in 16 days. 16 men together can complete the same work in 15 days. The ratio of the working capacity of a man to that of a woman is :
-
View Hint View Answer Discuss in Forum
20 × 16 women ≡ 16 × 15 men
⇒ 4 women ≡ 3 men⇒ men = 4 women 3
Hence, working capacity of man : woman = 4 : 3Correct Option: B
20 × 16 women ≡ 16 × 15 men
⇒ 4 women ≡ 3 men⇒ men = 4 women 3
Hence, working capacity of man : woman = 4 : 3
- A contractor undertakes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?
-
View Hint View Answer Discuss in Forum
Scheduled time to complete the work = 40 days
25 men in 24 days do 1 work 3
∴ 1 man in 1 day does1 = 1 work. 3 × 25 × 24 1800
Work remaining= 1 - 1 = 2 3 3
The work is to be completed 4 days before schedule i.e., in (40 – 4) 36 daysNo. of days left for 2 rd work 3
= 36 – 24 = 12 days1 1800
work is done in 1 day by 1 man.∴ 2 work will be done in 12 days by 3 1800 × 2 × 1 = 100 men 3 12
25 men are already working
∴ Extra men to be employed
= 100 – 25 = 75Correct Option: C
Scheduled time to complete the work = 40 days
25 men in 24 days do 1 work 3
∴ 1 man in 1 day does1 = 1 work. 3 × 25 × 24 1800
Work remaining= 1 - 1 = 2 3 3
The work is to be completed 4 days before schedule i.e., in (40 – 4) 36 daysNo. of days left for 2 rd work 3
= 36 – 24 = 12 days1 1800
work is done in 1 day by 1 man.∴ 2 work will be done in 12 days by 3 1800 × 2 × 1 = 100 men 3 12
25 men are already working
∴ Extra men to be employed
= 100 – 25 = 75
- Working efficiencies of P and Q for completing a piece of work are in the ratio 3 : 4. The number of days to be taken by them to complete the work will be in the ratio
-
View Hint View Answer Discuss in Forum
Using Rule 15,
Efficiency and time taken are inversely proportional.
∴ Required ratio = 4 : 3Correct Option: D
Using Rule 15,
Efficiency and time taken are inversely proportional.
∴ Required ratio = 4 : 3
- A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work?
-
View Hint View Answer Discuss in Forum
Let B alone do the work in x days.
∴ 6 × 1 + 3 × 1 = 1 12 x ⇒ 1 + 3 = 1 2 x ⇒ 3 = 1 ⇒ x = 6 days x 2 Correct Option: A
Let B alone do the work in x days.
∴ 6 × 1 + 3 × 1 = 1 12 x ⇒ 1 + 3 = 1 2 x ⇒ 3 = 1 ⇒ x = 6 days x 2
- A road of 5 km length will be constructed in 100 days. So 280 workers were employed. But after 80 days it was found that only
3 1 km road was completed. 2
Now how many more people were needed to finish the work in the specified time ?
-
View Hint View Answer Discuss in Forum
Using Rule 1,
Remaining work= 5 – 7 = 3 2 2
M1 × D1 × W2 = M2 × D2 × W1⇒ 280 × 80 × 3 2 = M2 × 20 × 7 2 ⇒ M2 = 280 × 80 × 3 = 480 20 × 7
∴ Required number of additional men = 480 – 280 = 200Correct Option: C
Using Rule 1,
Remaining work= 5 – 7 = 3 2 2
M1 × D1 × W2 = M2 × D2 × W1⇒ 280 × 80 × 3 2 = M2 × 20 × 7 2 ⇒ M2 = 280 × 80 × 3 = 480 20 × 7
∴ Required number of additional men = 480 – 280 = 200