Time And Work - Study Mode
[#166] A can do a piece of work in 6 days. B is 25% more efficient than A. How long would B alone take to finish this work ?
Correct Answer
(A) $${ ext{ 4}}frac{4}{5}{ ext{ days}}$$
Explanation
Solution: A : B Efficiency → 100% : 125% 4 : 5 Time 5 : 4 ×1.2↓ ↓×1.2 Actual time 6 days $${ ext{4}}frac{4}{5}$$ days
[#167] A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is = ?
Correct Answer
(B) 96 days
Explanation
Solution: Let time taken by B and C = x days ∴ Time taken by A = 3x days ∴ Part of work done by A, B and C in 1 day $$eqalign{
& = frac{1}{{ ext{x}}} + frac{1}{{3{ ext{x}}}} = frac{{3 + 1}}{{3{ ext{x}}}} = frac{4}{{3{ ext{x}}}} cr
& herefore frac{4}{{3{ ext{x}}}} = frac{1}{{24}} cr
& Rightarrow 3{ ext{x}} = 4 imes 24 cr
& Rightarrow { ext{x}} = frac{{4 imes 24}}{3} = 32,{ ext{days}} cr} $$ ∴ Time taken by A = 32 × 3 = 96 days. Alternet : Work done by all of them together in $$frac{1}{{24}}$$ Efficiency of A : Efficiency of (B + C) = 1 : 3 Work done by A in 1 day = $$frac{1}{{24}}$$ × $$frac{1}{{4}}$$ = $$frac{1}{{96}}$$ i.e., A alone can finish the job in 96 days. Alternet : Suppose A can complete the job in 3x days and (B + C) can complete the job in x days. $$eqalign{
& frac{{3{ ext{x}} imes { ext{x}}}}{{3{ ext{x}} + { ext{x}}}} = 24 cr
& Rightarrow frac{{3{ ext{x}}}}{4} = 24 cr
& Rightarrow { ext{x}} = 32 cr
& 3{ ext{x}} = 96,{ ext{days.}} cr} $$
[#168] Five men are working to complete a work in 15 days. After five days 10 women are accompanied by them to complete the work in next 5 days. If the work is to be done by women only, then in how many days could the work be over if 10 women have started it ?
Correct Answer
(C) 15 days
Explanation
Solution: 5 men's 15 day's work = 5 men's 10 day's work + 10 women's 5 day's work ⇒ 5 men's 5 day's work = 5 women's 5 day's work ⇒ 10 women's 5 day's work $$eqalign{
& = left( {frac{1}{{15}} imes 5}
ight) cr
& = frac{1}{3} cr} $$ ⇒ 10 women's 1 day's work = $$frac{1}{{15}}$$ ∴ 10 women can complete the work in 15 days.
[#169] A contractor undertake to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the work in men, how many days behind the scheduled the work should have been finished ?
Correct Answer
(A) 5
Explanation
Solution: 100 men's 40 day's work + 100 men's 5 day's work = 1 ⇒ 100 men's 45 day's work = 1 So, if the contractor had not engaged additional men, 100 men would have finished the work in 45 days. Difference in time = (45 - 40) = 5 days
[#170] A man, a woman and a boy can do a piece of work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day ?
Correct Answer
(D) 13
Explanation
Solution: (1 man + 1 woman)'s 1 day's work $$eqalign{
& = frac{1}{6} + frac{1}{9} cr
& = frac{5}{{18}} cr
& { ext{Remaining work}} cr
& = left( {1 - frac{5}{{18}}}
ight) cr
& = frac{{13}}{{18}} cr} $$ Work done by 1 boy in 1 day = $$frac{1}{{18}}$$ $$eqalign{
& herefore { ext{Number of boys required}} cr
& = left( {frac{{13}}{{18}} imes 18}
ight) cr
& = 13 cr} $$