Time And Work - Study Mode
[#226] 5 men and 2 women working together can do four times as much work per hour as a men and a women together. The work done by a men and a women should be in the ratio ?
Correct Answer
(B) 2 : 1
Explanation
Solution: $$frac{{{ ext{5 men}} + { ext{2 women}}}}{{4{ ext{work}}}}$$ xa0 xa0 = $$left( {1{ ext{ men}} + { ext{1 women}}}
ight)$$ $$5{ ext{ men}} + { ext{2 women}}$$ xa0 xa0 = $${ ext{4 men}} + { ext{4 women}}$$ $$eqalign{
& { ext{1 men}} = { ext{2 women}} cr
& frac{{{ ext{Men}}}}{{{ ext{Women}}}} = frac{2}{1} cr
& ,,,,,,,,,,,,,,,,,,{ ext{M}}:{ ext{W}} cr
& ,,,,,,,,,,,,,,,,,,,,,2:1 cr} $$
[#227] If 40 men or 60 women or 80 children can do a piece of work in 6 months, then 10 men, 10 women and 10 children together do the work in ?
Correct Answer
(D) $${ ext{11}}frac{1}{{13}}{ ext{ months}}$$
Explanation
Solution: 40 men = 60 women = 80 children 2 men = 3 women = 4 children 2 men = 3 women 1 women = $$frac{2}{3}$$ men → 10 women $$ o frac{2}{3} imes 10 = frac{{20}}{3}{ ext{ men}}$$ Similarly 2 men = 4 children 1 children = $$frac{1}{2}$$ men → 10 children $$,,,,,,,,,,,,,,,,,,,,,,,,,,, = frac{{10}}{2} = { ext{5 men}}$$ 10 men = 10 women = 10 children $$eqalign{
& { ext{10 men}} + frac{{20}}{3} + 5 cr
& Rightarrow frac{{30 + 20 + 15}}{3} cr} $$ 10 men + 10 women + 10 children = $$frac{{65}}{3}$$ men 40 men can do a piece of work in 6 months 1 men can do a piece of work in 6 × 40 $$frac{{65}}{3}$$ men can do a piece of work in $$eqalign{
& = frac{{6 imes 40}}{{frac{{65}}{3}}} cr
& = 11frac{1}{{13}}{ ext{ months}} cr} $$ Alternate : 40 men = 60 women = 80 children 2 men = 3 women = 4 children men : women : children = 6 : 4 : 3 (efficiency) ∴ Total work $$eqalign{
& = 40 imes 6 imes 6 cr
& = 1440,{ ext{units}} cr} $$ Total time taken by (40 men + 60 women + 80 children) $$eqalign{
& = frac{{{ ext{Total work}}}}{{{ ext{Efficiency}}}} cr
& = frac{{1440}}{{130}} cr
& = 11frac{1}{{13}}{ ext{months}} cr} $$
[#228] Two workers A and B working together completed a job in 5 days. If A had worked twice as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require?
Correct Answer
(C) $${ ext{7}}frac{1}{2}{ ext{ days}}$$
Explanation
Solution: L.C.M. of Total Work = 15 One day work of A + B = $$frac{{15}}{5}$$ = 3 unit/day One day work of (2A + B) = $$frac{{15}}{3}$$ = 5 unit/day Now, Assume A's efficiency is 2 units, B's is 1 unit. So, it satisfies the equation of both cases So, actual efficiency of A is 2 units/day A alone can complete the work in $$eqalign{
& = frac{{{ ext{Total work}}}}{{{ ext{Efficiency}}}} cr
& = frac{{15}}{2} cr
& = 7frac{1}{2}{ ext{days}} cr} $$
[#229] 3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job in ?
Correct Answer
(D) 20 days
Explanation
Solution: (3 men + 7 women) × 5 days = (4 men + 6 women) × 4 days 1 men = 11 women ∴ 3 men + 7 women (3 × 11) women + 7 women = 40 women 40 women can do a work in 5 days 1 women can do a work in (5 × 40) days 10 women can do a work in = $$frac{{5 imes 40}}{{10}}$$ = 20 days
[#230] P, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour ?
Correct Answer
(C) 15, 18, 21
Explanation
Solution: Let the number of pages typed in one hour by P, Q and R be x, y and z respectively Then, $$eqalign{
& Rightarrow x + y + z = frac{{216}}{4} cr
& Rightarrow x + y + z = 54z.....{ ext{(i)}} cr
& { ext{ }}z - y = y - x cr
& Rightarrow 2y = x + z.....{ ext{(ii)}} cr
& { ext{ }}5z = 7x cr
& Rightarrow x = frac{5}{7}z......{ ext{(iii)}} cr} $$ Solving (i), (ii) and (iii), we get $$eqalign{
& x = 15, cr
& y = 18,{ ext{ }} cr
& z = 21 cr} $$