Time And Work - Study Mode

[#136] X can copy 80 pages in 20 hours, x and y together can copy 135 pages in 27 hours. Then y can copy 20 pages in ?
Correct Answer

(A) 20 hours

Explanation

Solution: $$eqalign{
& Rightarrow {{ ext{R}}_{ ext{x}}} cr
& = frac{{80}}{{20}} cr
& { ext{ = 4 pages/hour}} cr
& Rightarrow {{ ext{R}}_{{ ext{x + y}}}} cr
& = frac{{135}}{{27}} cr
& { ext{ = 5 pages/hour}} cr
& Rightarrow {{ ext{R}}_{ ext{y}}} cr
& = {{ ext{R}}_{{ ext{x + y}}}} - {{ ext{R}}_{ ext{x}}} cr
& = 5 - 4 cr
& = 1{ ext{ pages/hour}} cr
& herefore { ext{y can copy 20 pages in}} cr
& = frac{{{ ext{20p}}}}{{{ ext{1p/h}}}} cr
& = { ext{ }}20{ ext{ hours}} cr} $$

[#137] A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C together for 2 days and A was replaced by B. In how many days, altogether, was the work complete ?
Correct Answer

(B) 8 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A}} + { ext{C}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{1}{{10}} + frac{1}{{20}}}
ight) cr
& = frac{3}{{20}} cr
& left( {{ ext{A}} + { ext{C}}}
ight){ ext{'s 2 day's work}} cr
& = left( {frac{3}{{20}} imes 2}
ight) cr
& = frac{3}{{10}} cr
& { ext{Remaining work }} cr
& = left( {1 - frac{3}{{10}}}
ight) cr
& = frac{7}{{10}}{ ext{ }} cr
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{1}{{15}} + frac{1}{{20}}}
ight) cr
& = frac{7}{{60}} cr} $$ $$frac{7}{{60}}$$ work is done by B and C in 1 day ∴ $$frac{7}{{10}}$$ work is done by B and C in $$eqalign{
& = left( {frac{{60}}{7} imes frac{7}{{10}}}
ight) cr
& = 6{ ext{ days}}{ ext{. }} cr
& { ext{Hence, total time taken }} cr
& = left( {2 + 6}
ight){ ext{days}} cr
& = 8{ ext{ days}} cr} $$

[#138] A completes $$frac{7}{{10}}$$ of the work 15 days. Then he completes the remaining work the help of B in 4 days. The time required for A and B together to complete the entire work is = ?
Correct Answer

(D) $$13frac{1}{3}{ ext{days}}$$

Explanation

Solution: $$eqalign{
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 4 day's work}} cr
& = left( {1 - frac{7}{{10}}}
ight) cr
& = frac{3}{{10}} cr
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{3}{{10}} imes frac{1}{4}}
ight) cr
& = frac{3}{{40}} cr
& { ext{Remaining work }} cr
& = left( {1 - frac{3}{{10}}}
ight) cr
& = frac{7}{{10}}{ ext{ }} cr
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{1}{{15}} + frac{1}{{20}}}
ight) cr
& = frac{7}{{60}} cr} $$ Hence, A an B together take $$ = frac{{40}}{3} = 13frac{1}{2}$$ xa0 days to complete the entire work.

[#139] A man and a boy can do a piece of work in 24 days. If the man works alone for the last 6 days, it is completed in 26 days. How long would the boy take to do it alone ?
Correct Answer

(D) 72 days

Explanation

Solution: (M + B)'s 1 day's work =$$frac{1}{{24}}$$ (M + B)'s 20 day's work + M's 6 day's work = 1 $$eqalign{
& Rightarrow { ext{M's 6 day's work}} cr
& = left( {1 - frac{1}{{24}} imes 20}
ight) cr
& = frac{4}{{24}} = frac{1}{6} cr
& Rightarrow { ext{M's 1 day's work}} cr
& = frac{1}{6} imes frac{1}{6} cr
& = frac{1}{{36}} cr
& herefore { ext{B's 1 day's work}} cr
& = frac{1}{{24}} - frac{1}{{36}} cr
& = frac{1}{{72}} cr} $$ Hence, the boy alone can do the work in 72 days.

[#140] Two men can do a piece of work in x days. But y women can do that in 3 days. Then the ratio of the work done by 1 man and 1 woman is ?
Correct Answer

(A) 3y : 2x

Explanation

Solution: 2 men can do a work in x days 1 men can do a work in (2 × x) days y women can do a work in 3 days 1 women can do a work in 3y days 1 man : 1 woman Days 2x : 3y Efficiency 3y : 2x $$eqalign{
& {x08f{Alternate:}} cr
& { ext{2M}} imes x = y{ ext{W}} imes { ext{3}} cr
& frac{{ ext{M}}}{{ ext{W}}} = frac{{3y}}{{2x}} cr
& { ext{M}}:{ ext{W}} = 3y:2x cr} $$