Time And Work - Study Mode

[#311] 18 men or 36 boys working 6 hours a day can plough a field in 24 days. In how many days will 24 men and 24 boys working 9 hours a day plough the same field ?
Correct Answer

(D) 8 days

Explanation

Solution: Let the required no of days be x. 18 Men = 36 Boys 1 Man = 2 Boys ∴ 24 Men = 48 Boys According to the question, M 1 D 1 H 1 = M 2 D 2 H 2 36 × 24 × 6 = (48 + 24) × x × 9 36 × 24 × 6 = 72 × 9 × x x = $$frac{{36 imes 6 imes 24}}{{72 imes 9}}$$ x = 8 days

[#312] A can do $$frac{1}{3}$$ rd of a work in 5 days and B can do the do $$frac{2}{5}$$ th of this work in 10 days. Both A and B, together can do the work in ?
Correct Answer

(C) $${ ext{9}}frac{3}{8}{ ext{ days}}$$

Explanation

Solution: $$eqalign{
& frac{1}{3}{ ext{work in 5 days}} cr
& { ext{then a complete work in}} cr
& = 5 imes 3 = 15{ ext{ days}} cr
& { ext{B}} o frac{2}{5}{ ext{work in 10 days}} cr
& { ext{then B completes work in}} cr
& = 10 imes frac{5}{2} = { ext{25 days}} cr} $$ L.C.M. of Total Work =75 One day work of A = $$frac{{75}}{{15}}$$ = 5 unit/day One day work of B = $$frac{{75}}{{25}}$$ = 3 unit/day $$eqalign{
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{ can do work}} cr
& = frac{{75}}{8} = 9frac{3}{8}{ ext{ days}} cr} $$

[#313] A and B undertake a piece of work for Rs. 250. A alone can do that work in 5 days and B alone can do that work in 15 days. With the help of C, they finish the work in 3 days. If every one gets paid in proportion to work done by them, the amount C will get is ?
Correct Answer

(A) Rs. 50

Explanation

Solution: L.C.M. of Total Work = 45 One day work of A = $$frac{{45}}{{5}}$$ = 9 unit/day One day work of B = $$frac{{45}}{{15}}$$ = 3 unit/day One day work of A + B + C = $$frac{{45}}{{3}}$$ = 15 unit/day $$eqalign{
& { ext{Efficiency of C}} cr
& = 15 - left( {9 + 3}
ight) cr
& = 3 cr
& { ext{C's amount}} cr
& = frac{{250}}{{15}} imes 3 cr
& = { ext{Rs}}{ ext{. 50}} cr} $$

[#314] A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work is = ?
Correct Answer

(D) 24 days

Explanation

Solution: $$eqalign{
& { ext{B}}:{ ext{A}} cr
& ,1:2 o { ext{Efficiency ratio}} cr
& { ext{Total work}} = 16 imes left( {1 + 2}
ight) = 48 cr} $$ Number of days taken by A to complete the work $$eqalign{
& = frac{{48}}{2} cr
& = 24{ ext{ days}} cr} $$

[#315] A contractor was engaged to construct a road in 16 days. After working for 12 days with 20 labours it was found that only $${frac{5}{8}}$$ th of the road had been constructed. To complete the work in stipulated time the number of extra labours required are ?
Correct Answer

(A) 16

Explanation

Solution: $$eqalign{
& { ext{From, }} cr
& frac{{{{ ext{m}}_1} imes {{ ext{d}}_1} imes {{ ext{t}}_1}}}{{{{ ext{w}}_1}}} = frac{{{{ ext{m}}_2} imes {{ ext{d}}_2} imes {{ ext{t}}_2}}}{{{{ ext{w}}_2}}} cr
& { ext{Let extra workers be x}} cr
& Rightarrow frac{{20 imes 12}}{{frac{5}{8}}} = frac{{left( {20 + x}
ight) imes 4}}{{frac{3}{8}}} cr
& Rightarrow 4 imes 12 = frac{{left( {20 + x}
ight) imes 4}}{3} cr
& Rightarrow 36 = 20 + x cr
& Rightarrow x = 16 cr
& Rightarrow { ext{Extra workers }} = { ext{16}} cr} $$