Unitary Method
- If 16 men working 7 hours day can plough a field in 48 days, in how many days will 14 men working 12 hours a clay plough the same field?
-
View Hint View Answer Discuss in Forum
16 men working 7 hours day can plough a field in 48 days.
1 men working 7 hours day can plough a field in 48 x 16 days.
1 men working 1 hours day can plough a field in 48 x 16 x 7 days.Correct Option: B
16 men working 7 hours day can plough a field in 48 days.
1 men working 7 hours day can plough a field in 48 x 16 days.
1 men working 1 hours day can plough a field in 48 x 16 x 7 days.
14 men working 1 hours day can plough a field in 48 x 16 x 7 / 14 days.
14 men working 12 hours day can plough a field in 48 x 16 x 7 / 14 x 12 days.
14 men working 12 hours day can plough a field in 48 x 16 / 2 x 12 days.
14 men working 12 hours day can plough a field in 48 x 4 / 2 x 3 days.
14 men working 12 hours day can plough a field in 48 x 2 / 3 days.
14 men working 12 hours day can plough a field in 16 x 2 = 32 days.
- If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
-
View Hint View Answer Discuss in Forum
7 spiders make 7 webs in 7 days.
∴ 1 spiders make 7 webs in 7 x 7 days.
....................................................................................................................Correct Option: B
7 spiders make 7 webs in 7 days.
∴ 1 spiders make 7 webs in 7 x 7 days.
∴ 1 spiders make 1 webs in 7 x 7 / 7 days.
∴ 1 spiders make 1 webs in 7 days.
- 40 men complete one-third of a work in 40 days. How many more men should be employed to finish the rest of the work in 50 more days ?
-
View Hint View Answer Discuss in Forum
Work done = 1/3
Remaining work = (1 - 1/3) = 2/3
Let the number of additional men be N. (Direct proportion)
More days, Less men (Indirect proportion)
Work 1/3 : 2/3
Days 50 : 40
∴ 1/3 x 50 x (40 + N) = 2/3 x 40 x 40Correct Option: D
Work done = 1/3
Remaining work = (1 - 1/3) = 2/3
Let the number of additional men be N. (Direct proportion)
More days, Less men (Indirect proportion)
Work 1/3 : 2/3
Days 50 : 40
∴ 1/3 x 50 x (40 + N) = 2/3 x 40 x 40
⇒ 5 x (40 + N) = 2 x 40 x 4
⇒ 200 + 5N = 320
⇒ 5N = 320 - 200 = 120
∴ N = 120/5 = 24
∴ Required number of men = 24
- 20 men complete one-third of a work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?
-
View Hint View Answer Discuss in Forum
Work done = 1/3
Remaining work = 1 - (1/3) = 2/3
Let the number of more men to be employed be N.
More work, More men (Direct proportion)
More days, Less men (Indirect proportion)
Work 1/3 : 2/3
Days 25 : 20
∴ 1/3 x 25 x (20 + N) = 2/3 x 20 x 20Correct Option: B
Work done = 1/3
Remaining work = 1 - (1/3) = 2/3
Let the number of more men to be employed be N.
More work, More men (Direct proportion)
More days, Less men (Indirect proportion)
Work 1/3 : 2/3
Days 25 : 20
∴ 1/3 x 25 x (20 + N) = 2/3 x 20 x 20
⇒ (20 + N) = 800/25 = 32
∴ N = 32 - 20 = 12
- 8 men can complete a work in 12 days, 4 women can complete it in 48 days and 10 children can complete the same work in 24 days. In how many days can 10 men, 4 women and 10 children complete the same work ?
-
View Hint View Answer Discuss in Forum
1 man can finish the work in (8 x 12) = 96 days
1 woman can finish the work in (4 x 48) = 192 days
1 child can finish the work in (10 x 24) = 240 days
1 man's 1 day's work = 1/96
1 women's 1 day's work = 1/192
1 child's 1 day's work = 1/240Correct Option: D
1 man can finish the work in (8 x 12) = 96 days
1 woman can finish the work in (4 x 48) = 192 days
1 child can finish the work in (10 x 24) = 240 days
1 man's 1 day's work = 1/96
1 women's 1 day's work = 1/192
1 child's 1 day's work = 1/240
(10 men + 4 women + 10 children)'s 1 day's work = (10/96 + 4/192 + 10/240)
= (5/48 + 1/48 + 1/24)
= (5 + 1 + 2)/48)
= 8/48 = 1/6
Hence, they will finish the work in 6 days.
