Time And Work - Study Mode
[#206] A alone can do $$frac{2}{5}$$ of a work in 12 days. B is 25 percent more efficient than A. C alone can do the same work in 12 days less than B. D is 25 percent less efficient than C. If they all work together, then the work will be completed in how many days?
Correct Answer
(B) $$frac{{240}}{{53}}$$
[#207] 4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can do it in 10 days. To complete the same work in 7 days, how many women should assist 4 men?
Correct Answer
(D) 13
Explanation
Solution: (4M + 5W) × 15 = (9M + 6W) × 10 12M + 15W = 18M + 12W $$frac{{ ext{M}}}{{ ext{W}}} = frac{1}{2}$$ (4M + xW) × 7 = (4 × 1 + 5 × 21 × 15) = Total work (4 × 1 + 2x) × 7 = 14 × 15 2x = 26
[#208] A and B can do a work in $$26frac{2}{3}$$xa0days. B and C together can complete the same work in 48 days, while A and C together can complete the same work in 30 days. How long (in days) will A alone take to complete 60% of the work?
Correct Answer
(A) 24
Explanation
Solution: $${ ext{A}} = 26frac{2}{3} = frac{{80}}{3}$$ 2(A + B + C) = 9 + 5 + 8 = 22 (A + B + C) = 11 A = 11 - 5 = 6 60% of total work $$ = frac{{60}}{{100}} imes 240 = 144$$ $${ ext{A}} = frac{{144}}{6} = 24{ ext{ days}}$$
[#209] A and B working together can do 30% of the work in 6 days. B alone can do the same Work in 25 days. How long will A alone take to complete the same work?
Correct Answer
(D) 100 days
Explanation
Solution: Required answer = $$frac{{100}}{{5 - 4}}$$ xa0= 100 days
[#210] A and B together can complete a piece of work in 15 days. B and C together can do it in 24 days. If A is twice as good a workman as C. Then in how many days can B alone complete the work?
Correct Answer
(B) 60 days
Explanation
Solution: $$eqalign{
& { ext{Let the efficiency of C}} = { ext{x and A}} = { ext{2x}} cr
& { ext{A}} + { ext{B}} = { ext{8}} cr
& { ext{B}} + { ext{C}} = { ext{5}} cr
& overline {,{ ext{A}} - { ext{C}} = 3,} cr
& 2{ ext{x}} - { ext{x}} = 3 cr
& { ext{x}} = 3 cr
& { ext{Efficiency of A}} = { ext{6, B}} = { ext{2, C}} = { ext{3}} cr
& { ext{Required answer}} cr
& { ext{B}} = frac{{120}}{2} = 60{ ext{ days}} cr} $$