Time And Work - Study Mode

[#261] A is 60% more efficient than B. In how many days will A and B working together complete a piece of work which A alone takes 15 days to finish?
Correct Answer

$$frac{{124}}{{13}}$$ days

Explanation

Solution: Given, A is 60% more efficient of B Means, $$eqalign{
& { ext{A}} = { ext{B}} + 60\% ,{ ext{of B}} cr
& { ext{A}} = { ext{B}} + frac{{60{ ext{B}}}}{{100}} cr
& { ext{A}} = frac{{100{ ext{B}} + 60{ ext{B}}}}{{100}} cr
& { ext{A}} = frac{{160{ ext{B}}}}{{100}} cr
& { ext{A}} = frac{{8{ ext{B}}}}{5} cr} $$ A can complete whole work in 15 days. So, One day work of A = $$frac{1}{{15}}$$ One day work of A = $$frac{{8{ ext{B}}}}{5}$$ = $$frac{1}{{15}}$$ One day work of B = $$frac{5}{{120}}$$xa0= $$frac{1}{{24}}$$ One day work, (A + B) = $$ frac{1}{{15}} + frac{1}{{24}}$$ One day work, (A + B) = $$frac{{24 + 15}}{{360}}$$ xa0 = $$frac{{39}}{{360}}$$ So, Time taken to finish the work by A and B together = $$frac{{360}}{{39}}$$ = $$frac{{120}}{{13}}$$ days Alternatively We can solve it through percentage method Given, A = $$frac{{8{ ext{B}}}}{5}$$ A can complete whole work in 15 days Work rate of A = $$frac{{100}}{{15}}$$ = 6.66% per day Work rate of $$frac{{8{ ext{B}}}}{5}$$ = 6.66% Work rate of B = 4.16% per day Work rate of (A + B) = 6.66 + 4.16 = 10.82% per day So, A and B can complete 100% work in $$frac{{120}}{{13}}$$ days

[#262] A pipe can fill a tank in 0.9 hours and another pipe can empty in 0.7 hours. If tank is completely filled and both pipes are opened simultaneously then 450 liters of water is removed from the tank is 2.5 hours. What is the capacity of the tank?
Correct Answer

(D) 567 liters

Explanation

Solution: Pipe A can fill the empty tank in = 0.9 hours So work rate of the Pipe A = $$frac{{100}}{{0.9}}$$ % per hour Pipe B can empty the tank in = 0.7 hours Negative Work rate of B = $$frac{{100}}{{0.7}}$$ % per hour. (B is removing water, so, taken as negative work) Tank fill per hour = $$frac{{100}}{{0.7}} - frac{{100}}{{0.9}}$$ xa0 = 31.75% per hour Time Taken to empty the tank = $$frac{{100}}{{31.75}}$$xa0 ≈ 3.15 hours So, Capacity of the tank = 3.15 × 180 = 567 liters

[#263] A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Correct Answer

(C) $$9frac{3}{5}$$ days

Explanation

Solution: $$eqalign{
& left( {{ ext{A + B + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{4} cr
& { ext{A's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{16}} cr
& { ext{B's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{12}} cr
& herefore { ext{C's}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = frac{1}{4} - left( {frac{1}{{16}} + frac{1}{{12}}}
ight) = {frac{1}{4} - frac{7}{{48}}} = frac{5}{{48}} cr
& { ext{So,}},{ ext{C}},,{ ext{alone}},{ ext{can}},{ ext{do}},{ ext{the}},{ ext{work}},{ ext{in}} cr
& frac{{48}}{5} = 9frac{3}{5},{ ext{days}} cr} $$

[#264] A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Correct Answer

(B) 15 days

Explanation

Solution: $$eqalign{
& { ext{A's}},{ ext{2}},{ ext{day's}},{ ext{work}} = {frac{1}{{20}} imes 2} = frac{1}{{10}} cr
& left( {{ ext{A + B + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{20}} + frac{1}{{30}} + frac{1}{{60}}} = frac{6}{{60}} = frac{1}{{10}} cr
& { ext{Work}},{ ext{done}},{ ext{in}},{ ext{3}},{ ext{days}} = {frac{1}{{10}} + frac{1}{{10}}} = frac{1}{5} cr
& { ext{Now}},,frac{1}{5},{ ext{work}},{ ext{is}},{ ext{done}},{ ext{in}},{ ext{3}},{ ext{days}} cr
& herefore { ext{Whole}},{ ext{work}},{ ext{will}},{ ext{be}},{ ext{done}},{ ext{in}}, cr
& {3 imes 5} = 15,{ ext{days}} cr} $$

[#265] A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Correct Answer

(B) $$22frac{1}{2}$$ days

Explanation

Solution: $$eqalign{
& { ext{Ratio}},{ ext{of}},{ ext{times}},{ ext{taken}},{ ext{by}},{ ext{A}},{ ext{and}},{ ext{B = 1:3}} cr
& { ext{The}},{ ext{time}},{ ext{difference}},{ ext{is}},left( {{ ext{3 - 1}}}
ight),{ ext{2}},{ ext{days}} cr
& { ext{while}},{ ext{B}},{ ext{take}},{ ext{3}},{ ext{days}},{ ext{and}},{ ext{A}},{ ext{takes}},{ ext{1}},{ ext{day}}{ ext{.}} cr
& { ext{If}},{ ext{difference}},{ ext{of}},{ ext{time}},{ ext{is}},{ ext{2}},{ ext{days,}},{ ext{B}},{ ext{takes}},{ ext{3}},{ ext{days}}{ ext{.}} cr
& { ext{If}},{ ext{difference}},{ ext{of}},{ ext{time}},{ ext{is}},{ ext{60}},{ ext{days,}} cr
& { ext{B}},{ ext{takes}},left( {frac{3}{2} imes 60}
ight) = 90,{ ext{days}} cr
& { ext{So,}},{ ext{A}},{ ext{takes}},{ ext{30}},{ ext{days}},{ ext{to}},{ ext{do}},{ ext{the}},{ ext{work}}{ ext{.}} cr
& { ext{A's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{30}} cr
& { ext{B's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{90}} cr
& left( {{ ext{A + B}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{30}} + frac{1}{{90}}} = frac{4}{{90}} = frac{2}{{45}} cr
& herefore { ext{A}},{ ext{and}},{ ext{B}},{ ext{together}},{ ext{can}},{ ext{do}},{ ext{the}},{ ext{work}},{ ext{in}}, cr
& frac{{45}}{2} = 22frac{1}{2},{ ext{days}}, cr} $$