Time And Work - Study Mode

[#141] If 12 carpenters working 6 hours a day can make 460 chairs in 240 days, then number of chairs made by 18 carpenters in 360 days each working 8 hours a day ?
Correct Answer

(B) 1380

Explanation

Solution: $${ ext{According to the question,}}$$ $$ Rightarrow frac{{12 imes 6 imes 240}}{{460}}$$ xa0 xa0 = $$frac{{18 imes 360 imes 8}}{x}$$ $$eqalign{
& Rightarrow x = frac{{18 imes 360 imes 8 imes 460}}{{12 imes 6 imes 240}} cr
& Rightarrow x = 1380 cr} $$

[#142] A company employed 200 workers to complete a certain work in 150 days. If only $$frac{1}{4}$$ th of the work had been done in 50 days, then in order to complete the whole work in time, the number of additional workers to be employed were ?
Correct Answer

(A) 100

Explanation

Solution: $$eqalign{
& Rightarrow frac{{{{ ext{M}}_1}{{ ext{D}}_1}}}{{{{ ext{W}}_1}}} = frac{{{{ ext{M}}_2}{{ ext{D}}_2}}}{{{{ ext{W}}_2}}} cr
& Rightarrow frac{{200 imes 50}}{{frac{1}{4}}} = frac{{{{ ext{M}}_2} imes 100}}{{frac{3}{4}}} cr
& Rightarrow {{ ext{M}}_2} = 300 cr
& { ext{So, additional men}} cr
& = 300 - 200 cr
& = 100 cr} $$

[#143] If 20 women can lay a road of length 100m in 10 days. 10 women can lay the same road of length 50m in = ?
Correct Answer

(C) 10 days

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& frac{{20 imes 10}}{{100}} = frac{{10 imes x}}{{50}} cr
& Leftrightarrow x = 10{ ext{ days}} cr} $$

[#144] A and B can together finish a work in 30 days. They worked together for 20 days and B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ?
Correct Answer

(D) 60 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 20 day's work}}{ ext{.}} cr
& = left( {frac{1}{{30}} imes 20}
ight) cr
& = frac{2}{3} cr
& { ext{Remaining work }} cr
& = left( {1 - frac{2}{3}}
ight) cr
& = frac{1}{3}{ ext{ }} cr} $$ Now, $$frac{1}{3}$$ work is done by A in 20 days Whole work will be done by A in (20 × 3) = 60 days.

[#145] A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall ?
Correct Answer

(C) $${ ext{7}}frac{1}{3}{ ext{ days}}$$

Explanation

Solution: Part of wall built by A in 1 day = $$frac{1}{8}$$ Part of wall broken by B in 1 day = $$frac{1}{3}$$ Part of wall built by A in 4 days $$eqalign{
& = left( {frac{1}{8} imes 4}
ight) cr
& = frac{1}{2} cr} $$ Part of wall broken by B and built by A in 2 days $$eqalign{
& = 2left( {frac{1}{3} - frac{1}{8}}
ight) cr
& = frac{5}{{12}} cr} $$ $$eqalign{
& { ext{Part of wall built in 6 days}} cr
& = left( {frac{1}{2} - frac{5}{{12}}}
ight) cr
& = frac{1}{{12}} cr
& { ext{Remaining part to be built}} cr
& = left( {1 - frac{1}{{12}}}
ight) cr
& = frac{{11}}{{12}} cr} $$ Now, $$frac{1}{8}$$ part of wall built by A in 1 day $$eqalign{
& herefore frac{{11}}{{12}}{ ext{ part of wall built by A in}} cr
& = left( {8 imes frac{{11}}{{12}}}
ight) cr
& = frac{{22}}{3} cr
& = 7frac{1}{3}{ ext{ day}} cr} $$