Time And Work - Study Mode

[#196] A is twice as efficient as B, and they take equal time as the time taken by C and D to do this work together. If C and D can complete the same work in 15 and 20 days respectively, then. In how many days can A alone complete the work?
Correct Answer

(B) $$frac{{90}}{7}$$

Explanation

Solution: A = 2B B = $$frac{{ ext{A}}}{2}$$ Efficiency of (A + B) = Efficiency of (C + D) $$eqalign{
& { ext{A}} + { ext{B}} = 7 cr
& Rightarrow { ext{A}} + frac{{ ext{A}}}{2} = 7 cr
& Rightarrow { ext{A}} = frac{{14}}{3} cr
& { ext{Time of A}} = frac{{60 imes 3}}{{14}} = frac{{90}}{7}{ ext{Answer}} cr} $$

[#197] A can do $$frac{1}{4}$$ part of a work in 9 days. B can do $$frac{2}{3}$$ part of the same work in 28 days. Working together, in how many days can A and B complete the whole work?
Correct Answer

(A) $$frac{{252}}{{13}}{ ext{ days}}$$

Explanation

Solution: (A + B) = $$frac{{252}}{{13}}$$

[#198] Three painters have to spend 6 hours a day for 12 days to finish a work. If after 3 days one painter leaves, in how many days the remaining work will be completed?
Correct Answer

(B) $$13frac{1}{2}$$

Explanation

Solution: M 1 D 1 H 1 Remaining work of three painters of (12 - 3) days is completed by two painters 3 × 9 × 6 = 2 × 6 × D 2 D 2 = $$13frac{1}{2}$$xa0days

[#199] If one man or two women or four boys or five girls can finish a work in 39 days, then how many days will one man, one woman, one boy and one girl together take to finish the same work?
Correct Answer

(D) 20

Explanation

Solution: Man × 39 = 2 Women × 39 = 4 Boys × 39 = 5 Girls × 39 [x08egin{array}{*{20}{c}}
{}&x08egin{gathered}
{ ext{M}} hfill \
, downarrow hfill \
{ ext{20}} hfill \
end{gathered} &x08egin{gathered}
= hfill \
hfill \
hfill \
end{gathered} &x08egin{gathered}
{ ext{2W}} hfill \
,, downarrow hfill \
{ ext{10}} hfill \
end{gathered} &x08egin{gathered}
= hfill \
hfill \
hfill \
end{gathered} &x08egin{gathered}
{ ext{4B}} hfill \
,, downarrow hfill \
,,5 hfill \
end{gathered} &x08egin{gathered}
= hfill \
hfill \
hfill \
end{gathered} &x08egin{gathered}
{ ext{5G}} hfill \
,, downarrow hfill \
,,4 hfill \
end{gathered} \
{{ ext{Efficiency}} o }&{ ext{M}}&{}&{ ext{W}}&{}&{,,{ ext{B}}}&{}&{,,{ ext{G}}}
end{array}] Total work = 20 × 39 20 × 39 = (M + W + B + G) × d 20 × 39 = 39 × d d = 20 days

[#200] A and B can do a piece of work in 25 days. B alone can do $$66frac{2}{3}\% $$ xa0of the same work in 30 days. In how many days can A alone do $$frac{4}{{15}}$$ part of the same work?
Correct Answer

(A) 15

Explanation

Solution: $$eqalign{
& 66frac{2}{3}\% o 30{ ext{ days}} cr
& frac{2}{3} o 30{ ext{ days}} cr
& 1 o 45{ ext{ days}} cr} $$ $$eqalign{
& { ext{A}} = 4{ ext{ unit}} cr
& { ext{A}} = frac{{25 imes frac{4}{{15}}}}{4} cr
& { ext{A}} = 15{ ext{ days}} cr} $$