Time And Work - Study Mode

[#251] If 4 men or 6 women can do a piece of work in 12 days working 7 hours a day, how many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day ?
Correct Answer

(B) 7 days

Explanation

Solution: According to the question, 4 men = 6 women 2 men = 3 women 10 men + 3 women = 10 men + 2 men 10 men + 3 women = 12 men.....(i) $$frac{{{4_{{ ext{men}}}} imes {{12}_{{ ext{days}}}} imes {7_{{ ext{hours}}}}}}{{{{ ext{1}}_{{ ext{work}}}}}} = $$ xa0 xa0 xa0$$frac{{{{12}_{{ ext{men}}}} imes {{ ext{D}}_{{ ext{days}}}} imes {8_{{ ext{hours}}}}}}{{{{ ext{1}}_{{ ext{work}}}}}}$$ $$eqalign{
& { ext{After solving we get}} cr
& { ext{D}} = 7{ ext{ days}} cr} $$

[#252] A contractor undertook to finish a work in 92 days and employed 110 men. After 48 days, he found that he had already done $$frac{3}{5}$$ part of the work, the number of men he can withdraw so that his work may still be finished in time is ?
Correct Answer

(D) 30

Explanation

Solution: Let 'n' number of men can be withdrawn $$eqalign{
& frac{{left( {{{110}_{{ ext{men}}}} imes {{48}_{{ ext{days}}}}}
ight)}}{{frac{3}{5}{ ext{work}}}} = frac{{left( {110 - { ext{n}}}
ight) imes 44}}{{frac{2}{5}{ ext{work}}}} cr
& Rightarrow 110 imes 16 = left( {110 - { ext{n}}}
ight) imes 22 cr
& Rightarrow 160 = left( {110 - { ext{n}}}
ight) imes 2 cr
& Rightarrow { ext{n}} = 30 cr} $$

[#253] A man undertakes to do a certain work in 150 days. He employs 200 men. He finds that only a quarter of the work is done in 50 days. The number of additional men that should be appointed so that the whole work will be finished in time is = ?
Correct Answer

(B) 100

Explanation

Solution: Let 'n' number of men can required $$eqalign{
& frac{{left( {{{200}_{{ ext{men}}}} imes {{50}_{{ ext{days}}}}}
ight)}}{{frac{1}{4}}} = frac{{left( {200 + { ext{n}}}
ight) imes {{100}_{{ ext{days}}}}}}{{frac{3}{4}}} cr
& Rightarrow 3 imes 100 = left( {200 + { ext{n}}}
ight) cr
& Rightarrow { ext{n}} = 100 cr} $$

[#254] A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is ?
Correct Answer

(C) 15 days

Explanation

Solution: $$eqalign{
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{1}{{20}} + frac{1}{{30}}}
ight) cr
& = frac{5}{{60}} cr
& = frac{1}{{12}} cr
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 2 day's work}} cr
& = left( {frac{1}{{12}} imes 2}
ight) cr
& = frac{1}{6} cr
& { ext{Remaining work }} cr
& = left( {1 - frac{1}{6}}
ight) cr
& = frac{5}{6}{ ext{ }} cr
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{1}{{12}} + frac{1}{{15}}}
ight) cr
& = frac{9}{{60}} cr
& = frac{3}{{20}} cr} $$ Now, $$frac{1}{{18}}$$ work is done by A in 1 day $$eqalign{
& herefore frac{5}{6}{ ext{ work is done by A in }} cr
& = left( {18 imes frac{5}{6}}
ight) cr
& = 15{ ext{ days}} cr} $$

[#255] A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for B alone to paint the house?
Correct Answer

(C) 96

Explanation

Solution: A = 3B [ herefore frac{{ ext{A}}}{{ ext{B}}} = frac{3}{1}x08egin{array}{*{20}{c}}
{ imes 2} \
{ imes 2}
end{array}] [frac{{ ext{C}}}{{{ ext{A}} + { ext{B}} + { ext{C}}}} = frac{1}{3}x08egin{array}{*{20}{c}}
{ imes 4} \
{ imes 4}
end{array}] Efficiency :- A + B + C [x08egin{array}{*{20}{c}}
{ ext{A}}&{ ext{B}}&{ ext{C}} \
{}&{12}&6 \
2&4&{}
end{array}] ∵ A + B + C do work in 16 days Total work = 12 × 16 ∴ B will do work in $$ = frac{{12 imes 16}}{2} = 96{ ext{ days}}$$