Time And Work - Study Mode

[#161] A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
Correct Answer

(C) 12 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A + B}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{15}} + frac{1}{{10}}} = frac{1}{6} cr
& { ext{Work}},{ ext{done}},{ ext{by}},{ ext{A}},{ ext{and}},{ ext{B}},{ ext{in}},{ ext{2}},{ ext{days}} cr
& = {frac{1}{6} imes 2} = frac{1}{3} cr
& { ext{Remaining}},{ ext{work}} cr
& = {1 - frac{1}{3}} = frac{2}{3} cr
& { ext{Now}},,frac{1}{{15}},{ ext{work}},{ ext{is}},{ ext{done}},{ ext{by}},{ ext{A}},{ ext{in}},{ ext{1}},{ ext{day}} cr
& herefore frac{2}{3},{ ext{work}},{ ext{will}},{ ext{be}},{ ext{done}},{ ext{by}},{ ext{a}},{ ext{in}} cr
& {15 imes frac{2}{3}} = 10,{ ext{days}} cr
& { ext{Hence,}},{ ext{the}},{ ext{total}},{ ext{time}},{ ext{taken}} cr
& = {10 + 2} = 12,{ ext{days}} cr} $$

[#162] A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Correct Answer

(A) 18 days

Explanation

Solution: $$eqalign{
& { ext{2(A + B + C)'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{30}} + frac{1}{{24}} + frac{1}{{20}}} cr
& = frac{{15}}{{120}} = frac{1}{8} cr
& herefore left( {{ ext{A + B + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = frac{1}{{2 imes 8}} = frac{1}{{16}} cr
& { ext{Work}},{ ext{done}},{ ext{by}},{ ext{A,}},{ ext{B,}},{ ext{C}},{ ext{in}},{ ext{10}},{ ext{days}} cr
& = frac{{10}}{{16}} = frac{5}{8} cr
& { ext{Remaining}},{ ext{work}} cr
& = {1 - frac{5}{8}} = frac{3}{8} cr
& { ext{A's}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{16}} - frac{1}{{24}}} = frac{1}{{48}} cr
& { ext{Now}},,frac{1}{{48}},{ ext{work}},{ ext{isdone}},{ ext{by}},{ ext{A}},{ ext{in}},{ ext{1}},{ ext{day}} cr
& { ext{So}},,frac{3}{8},{ ext{work}},{ ext{will}},{ ext{be}},{ ext{done}},{ ext{by}},{ ext{A}},{ ext{in}} cr
& {48 imes frac{3}{8}} = 18,{ ext{days}} cr} $$

[#163] Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
Correct Answer

(B) 4 : 3

Explanation

Solution: $$eqalign{
& left( {20 imes 16}
ight){ ext{women}},{ ext{can}},{ ext{complete}},{ ext{the}},{ ext{work}},{ ext{in}},{ ext{1}},{ ext{day}} cr
& herefore { ext{1}},{ ext{woman's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{320}} cr
& left( {16 imes 15}
ight),{ ext{men}},{ ext{can}},{ ext{complete}},{ ext{the}},{ ext{work}},{ ext{in}},{ ext{1}},{ ext{day}} cr
& herefore { ext{1}},{ ext{man's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{240}} cr
& { ext{So,}},{ ext{required}},{ ext{ratio}} cr
& = frac{1}{{240}}:frac{1}{{320}} cr
& = frac{1}{3}:frac{1}{4} cr
& = 4:3,left( {{ ext{cross}},{ ext{multiplied}}}
ight) cr} $$

[#164] A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
Correct Answer

(C) 8 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A + B + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{6} cr
& left( {{ ext{A + B}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{8} cr
& left( {{ ext{B + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{12}} cr
& herefore left( {{ ext{A + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = left( {2 imes frac{1}{6}}
ight) - left( {frac{1}{8} + frac{1}{{12}}}
ight) cr
& = {frac{1}{3} - frac{5}{{24}}} cr
& = frac{3}{{24}} cr
& = frac{1}{8} cr }$$ So, A and C together will do the work in 8 days

[#165] A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
Correct Answer

(C) 10 days

Explanation

Solution: $$eqalign{
& left( {{ ext{B + C}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{9} + frac{1}{{12}}} = frac{7}{{36}} cr
& { ext{Work}},{ ext{done}},{ ext{by}},{ ext{B}},{ ext{and}},{ ext{C}},{ ext{in}},{ ext{3}},{ ext{days}} cr
& = {frac{7}{{36}} imes 3} = frac{7}{{12}} cr
& { ext{Remaining}},{ ext{work}} cr
& = {1 - frac{7}{{12}}} = frac{5}{{12}} cr
& { ext{Now}},,frac{1}{{24}},{ ext{work}},{ ext{is}},{ ext{done}},{ ext{by}},{ ext{A}},{ ext{in}},{ ext{1}},{ ext{day}} cr
& { ext{So}},,frac{5}{{12}},{ ext{work}},{ ext{is}},{ ext{done}},{ ext{by}},{ ext{A}},{ ext{in}} cr
& {24 imes frac{5}{{12}}} = 10,{ ext{days}} cr} $$