Time And Work - Study Mode

[#176] A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in = ?
Correct Answer

(C) 8 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A}} + { ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} = frac{1}{6} cr
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 1 day's work}} = frac{1}{8} cr
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} = frac{1}{{12}}{ ext{ }} cr
& herefore left( {{ ext{A}} + { ext{C}}}
ight){ ext{'s 1 day's work}} cr
& = left( {2 imes frac{1}{6}}
ight) - left( {frac{1}{8} + frac{1}{{12}}}
ight) cr
& = left( {frac{1}{3} - frac{5}{{24}}}
ight) cr
& = frac{3}{{24}} cr
& = frac{1}{8} cr} $$ So, A and C together will do the work in 8 days.

[#177] 10 men working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the same work in 12 days ?
Correct Answer

(A) 6 hours/day

Explanation

Solution: $$eqalign{
& frac{{{{10}_{{ ext{men}}}} imes {6_{{ ext{hours}}}} imes {{18}_{{ ext{days}}}}}}{{{1_{{ ext{work}}}}}} = frac{{{{15}_{{ ext{men}}}} imes {{12}_{{ ext{days}}}} imes { ext{H hour/day}}}}{{{1_{{ ext{work}}}}}} cr
& Leftrightarrow { ext{6 hours/day}} cr} $$

[#178] A work could be completed in 100 days by some workers. However, due to the absence of 10 workers, it was completed in 110 days. The original number of workers was ?
Correct Answer

(B) 110

Explanation

Solution: Let total number of worker in beginning is N $$eqalign{
& { ext{According to the question,}} cr
& frac{{{ ext{N}} imes {{100}_{{ ext{days}}}}}}{{{1_{{ ext{work}}}}}} = frac{{left( {{ ext{N}} - 10}
ight) imes {{110}_{{ ext{days}}}}}}{{{1_{{ ext{work}}}}}} cr
& 100{ ext{N}} = { ext{110N}} - { ext{1100}} cr
& Rightarrow { ext{10N}} = { ext{1100}} cr
& Rightarrow { ext{N}} = { ext{110}} cr} $$

[#179] A job can be complete by 12 men in 12 days. How many extra days will be needed to complete the job if 6 men leave after working for 6 days ?
Correct Answer

(B) 6 days

Explanation

Solution: According to the question, Total work = 12 M × 12 D = 144 units Work done by 12 men in 6 days = 12 × 6 = 72 units Rest work = 144 - 72 = 72 units Required time for 6 men to complete the work $$eqalign{
& = frac{{72}}{6} cr
& { ext{ = 12 days}} cr
& { ext{Hence,}} cr
& { ext{Total time}} = 12 + 6 = 18{ ext{ days}} cr
& { ext{Extra time}} = 18 - 12 = 6{ ext{ days}} cr} $$

[#180] 60 men could complete a piece of work in 250 days. They worked together for 200 days. After that work had to be stopped for 10 days due to bad weather. How many more men should be engaged to complete the work in time ?
Correct Answer

(B) 15

Explanation

Solution: 60 men work for 200 days. They stops for 10 day due to bad weather. So, the work is to complete in = (50 - 10) = 40 days In order to complete in scheduled time i.e., 250 days. Let 'n' number of more men is required (60 men × 200 days ) +{(60 + n) men × 40 days } = 60 men × 250 days ⇒ 12000 + {(60 + n) men × 40 days } = 15000 ⇒ (60 + n)40 days = 3000 ⇒ 60 + n = 75 ⇒ n = 15 Alternate : 60 men can complete a work in 250 days. But they work for 200 days. Then remaining days = 50 days So, 60 × 50 = 60 + x × 40 ⇔ x = 15