Time And Work - Study Mode

[#131] 25 men with 10 boys can do in 6 days as much work as 21 men with 30 boys can do in days. How many boys must help 40 men to do the same work in 4 days ?
Correct Answer

(B) 10

Explanation

Solution: $$eqalign{
& { ext{Let 1 men's 1 day's work}} = x cr
& { ext{and 1 boy's 1 day's work}} = y cr
& { ext{Then, }} cr
& Rightarrow { ext{6}}left( {25x + 10y}
ight) = 5left( {21x + 30y}
ight) cr
& Rightarrow 150x + 60y = 105x + 150y cr
& Rightarrow 45x = 90y cr
& Rightarrow x = 2y cr
& { ext{Let,}} cr
& { ext{The required number of boys be }}z cr
& { ext{Then,}} cr
& Rightarrow { ext{4}}left( {40x + zy}
ight) = 6left( {25x + 10y}
ight) cr
& Rightarrow 4left( {80y + zy}
ight) = 6left( {50y + 10y}
ight) cr
& Rightarrow 80 + z = frac{{6 imes 60}}{4} = 90 cr
& Rightarrow z = 10 cr} $$

[#132] 40 men can complete a piece of work in 15 days. 20 more men joined them after 5 days they start doing work. How many days will be required by them to finish the remaining work ?
Correct Answer

(D) $${ ext{6}}frac{2}{3}{ ext{ days}}$$

Explanation

Solution: Work done by 40 men in 5 days = $$frac{1}{3}$$ (As if whole work is completed in 15 days then in 5 days $${{{frac{1}{3}}^{{ ext{rd}}}}}$$ of the work will be finished) $$eqalign{
& { ext{Remaining work}} = 1 - frac{1}{3} = frac{2}{3} cr
& x08ecause 40{ ext{ men do 1 work in 15 days}}{ ext{.}} cr
& { ext{60 men can do }}frac{2}{3}{ ext{work in }}x{ ext{ day}} cr
& frac{{{{ ext{M}}_1}{{ ext{D}}_1}}}{{{{ ext{W}}_1}}}{ ext{ = }}frac{{{{ ext{M}}_2}{{ ext{D}}_2}}}{{{{ ext{W}}_2}}} cr
& {{ ext{M}}_1} = 40{ ext{ , }}{{ ext{M}}_2} = 60 cr
& {{ ext{D}}_1} = 15{ ext{ , }}{{ ext{D}}_2} = x cr
& {{ ext{W}}_1} = 1{ ext{ ,}}{{ ext{W}}_2} = frac{2}{3} cr
& Rightarrow frac{{40 imes 15}}{1} = frac{{60 imes x}}{2} cr
& Rightarrow frac{2}{3}left( {40 imes 15}
ight) = 60x cr
& Rightarrow 2 imes 40 imes 5 = 60x cr
& Rightarrow x = frac{{20}}{3} cr
& Rightarrow x = 6frac{2}{3}{ ext{ days}} cr} $$

[#133] A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternatively, with A beginning, then the work will be completed in ?
Correct Answer

(B) 11 days

Explanation

Solution: L.C.M. of Total Work = 45 One day work of A = $$frac{{45}}{{9}}$$ = 5 unit/day One day work of B = $$frac{{45}}{{15}}$$ = 3 unit/day $$eqalign{
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 2 days work }} cr
& = 5 + 3 cr
& = 8{ ext{ units}} cr
& { ext{They will do in }} cr
& = frac{{40}}{8} imes 2 cr
& = left( {5 imes 2}
ight) cr
& = 10{ ext{ days}} cr
& herefore { ext{Work left}} cr
& = 45 - 40 cr
& = { ext{5 units}} cr
& { ext{Now,}} cr
& { ext{A's turn and he will complete in}} cr
& = frac{5}{5} cr
& = 1{ ext{ days}} cr
& { ext{Then total work completed in}} cr
& = 10 + 1 cr
& = 11{ ext{ days}} cr} $$

[#134] 12 monkeys can eat 12 bananas in 12 minutes. In how many minutes can 4 monkeys eat 4 bananas ?
Correct Answer

(C) 12 minutes

Explanation

Solution: $$eqalign{
& { ext{Let the required time}} = { ext{T}} cr
& Rightarrow frac{{{{ ext{m}}_{ ext{1}}} imes {{ ext{d}}_{ ext{1}}} imes {{ ext{t}}_{ ext{1}}}}}{{{{ ext{w}}_{ ext{1}}}}}{ ext{ = }}frac{{{{ ext{m}}_{ ext{2}}} imes {{ ext{d}}_{ ext{2}}} imes {{ ext{t}}_{ ext{2}}}}}{{{{ ext{w}}_{ ext{2}}}}} cr
& Rightarrow frac{{12 imes 12}}{{12}} = frac{{4 imes { ext{time}}}}{4} cr
& Rightarrow { ext{Time}} = 12operatorname{minutes} cr} $$

[#135] Two worker A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work that when work together. If B worked alone, would take $${ ext{4}}frac{1}{2}$$ hours more than when working together. The time required to finish the work together is = ?
Correct Answer

(D) 6 hours

Explanation

Solution: $$eqalign{
& { ext{Let,}} cr
& { ext{a}} = { ext{8h}} cr
& { ext{b}} = { ext{4}}frac{1}{2}{ ext{h}} = frac{9}{2}{ ext{h}} cr} $$ Time required to finish the work together $$eqalign{
& = sqrt {{ ext{ab}}} cr
& = sqrt {8 imes frac{9}{2}} cr
& = 6{ ext{ h}} cr} $$