Time And Work - Study Mode

[#96] 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Correct Answer

(C) 7

Explanation

Solution: $$eqalign{
& 1,woman's,1,day's,work = frac{1}{{70}} cr
& { ext{1}},{ ext{child's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{140}} cr
& left( {{ ext{5}},{ ext{women + 10}},{ ext{children}}}
ight){ ext{'s}},{ ext{day's}},{ ext{work}} cr
& = {frac{5}{{70}} + frac{{10}}{{140}}} = {frac{1}{{14}} + frac{1}{{14}}} = frac{1}{7} cr
& herefore { ext{5}},{ ext{women}},{ ext{and}},{ ext{10}},{ ext{chidren}},{ ext{will}},{ ext{complete}} cr
& { ext{the}},{ ext{work}},{ ext{in}},{ ext{7}},{ ext{days}} cr} $$

[#97] X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Correct Answer

(B) 10 days

Explanation

Solution: $$eqalign{
& { ext{work}},{ ext{done}},{ ext{by}},{ ext{X}},{ ext{in}},{ ext{4}},{ ext{days}} cr
& = {frac{1}{{20}} imes 4} = frac{1}{5} cr
& { ext{Remaining}},{ ext{work}} cr
& = {1 - frac{1}{5}} = frac{4}{5} cr
& left( {{ ext{X + Y}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{20}} + frac{1}{{12}}} = frac{8}{{60}} = frac{2}{{15}} cr
& { ext{Now}},frac{2}{{15}}{ ext{work}},{ ext{is}},{ ext{done}},{ ext{by}},{ ext{X}},{ ext{and}},{ ext{Y}},{ ext{in}},{ ext{1}},{ ext{day}}. cr
& { ext{So}},,frac{4}{5},{ ext{work}},{ ext{will}},{ ext{be}},{ ext{done}},{ ext{by}},{ ext{X}},{ ext{and}},{ ext{Y}},{ ext{in}} cr
& {frac{{15}}{2} imes frac{4}{5}} = 6,{ ext{days}} cr
& { ext{Hence,}},{ ext{total}},{ ext{time}},{ ext{taken}} cr
& = left( {6 + 4}
ight),{ ext{days}} cr
& = 10,{ ext{days}} cr} $$

[#98] A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Correct Answer

(B) 13 days

Explanation

Solution: $$eqalign{
& { ext{Ratio}},{ ext{of}},{ ext{times}},{ ext{taken}},{ ext{by}},{ ext{A}},{ ext{and}},{ ext{B}} cr
& = 100:130 = 10:13 cr
& { ext{Suppose}},{ ext{B}},{ ext{takes}},x,{ ext{days}},{ ext{to}},{ ext{do}},{ ext{the}},{ ext{work}} cr
& { ext{Then}},10:13::23:x cr
& Rightarrow x = {frac{{23 imes 13}}{{10}}} cr
& Rightarrow x = frac{{299}}{{10}} cr
& { ext{A's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{1}{{23}} cr
& { ext{B's}},{ ext{1}},{ ext{day's}},{ ext{work}} = frac{{10}}{{299}} cr
& left( {{ ext{A + B}}}
ight){ ext{'s}},{ ext{1}},{ ext{day's}},{ ext{work}} cr
& = {frac{1}{{23}} + frac{{10}}{{299}}} cr
& = frac{{23}}{{299}} cr
& = frac{1}{{13}} cr
& herefore A,{ ext{and}},{ ext{B}},{ ext{together}},{ ext{can}},{ ext{complete}} cr
& ,{ ext{the}},{ ext{work}},{ ext{in}},{ ext{13}},{ ext{days}}{ ext{.}} cr} $$

[#99] There is provision of food in fort for 1200 soldiers for 60 days. After 15 days, 200 soldiers leave the fort. Remaining food will last for how many days?
Correct Answer

(C) 54 days

Explanation

Solution: Work equivalence method: 1200 × 45 = 1000 × x Hence, x = 54 days Variation Method: After 15 days 200 soldiers leaved. Soldiers xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0Food for days 1200 ↓ xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa045 1000 xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0xa0↑ x (let) Arrows show the opposite variation to each other $$frac{{1200}}{{1000}} = frac{{ ext{x}}}{{45}}$$ Or, x = $$frac{{1200 imes 45}}{{1000}}$$ xa0 = 54 days.

[#100] A and B working together completed a job in 5 days. If A works twice as efficiently as he actually did and B works $$frac{1}{3}$$ of actual efficiency, the work would have completed in 3 days. Find the for A to complete the job alone.
Correct Answer

(B) $$6frac{1}{4}$$

Explanation

Solution: One Day's work of A and B together, $$frac{1}{{ ext{A}}} + frac{1}{{ ext{B}}} = frac{1}{5},........({ ext{i}})$$ When A works with twice efficiency,Then, $$frac{2}{{ ext{A}}} + frac{1}{{3{ ext{B}}}} = frac{1}{3},........({ ext{ii}})$$ on solving equations (i) and (ii), we get $$A = frac{{25}}{4} = 6frac{1}{4}$$