Time And Work - Study Mode

[#121] If 450 men can finish construction of an apartment in 20 days, then how many men are needed to complete the same work in 30 days?
Correct Answer

(B) 300

Explanation

Solution: 450 men × 20 = x men × 30 x = 300 men

[#122] A can do $$frac{1}{3}$$ of a work in 30 days, B can do $$frac{2}{5}$$ of the same work in 24 days. They worked together for 20 days. C complete the remaining work in 8 days. Working together A, B and C will complete the same work in:
Correct Answer

(D) 12 days

Explanation

Solution: ⇒ A can do $$frac{1}{3}$$ of a work in 30 day ⇒ A completed work in 90 days ⇒ B can do $$frac{2}{5}$$ of the same work in 24 days ⇒ B can completed work in 60 days ⇒ Let the total work = LCM (90, 60) = 180 unit ⇒ Efficiency of A = 3 unit/day ⇒ Efficiency of B = 2 unit/day ⇒ They both worked for 20 days, work done in 20 days = 20 × 5 = 100 unit ⇒ Remaining work = 180 - 100 = 80 unit ⇒ Remaining work done by C in 8 days ⇒ Efficiency of C = 10 unit/day ⇒ Efficiency of (A + B + C) = 15 unit/day ⇒ Work completed = $$frac{{180}}{{15}}$$ = 12 days ∴ If all worked together, the work complete in 12 days.

[#123] X, Y and Z can do a piece of work in 46 days, 92 days and 23 days, respectively. X started the work. Y joined him after 2 days. If Z joined them after 8 days from the beginning, then for how many days did X work?
Correct Answer

(C) 18

Explanation

Solution: 2 days work of X = 2 × 2 = 4 After Y joined X and Y work 6 days = 3 × 6 = 18 After 8 days from begging - X, Y and Z work together $$ = frac{{92 - 22}}{7} = frac{{70}}{7} = 10{ ext{ days}}$$ Total days work of X = 10 + 8 = 18 days

[#124] A, B and C can all together do a piece of work in 10 days, in which B takes 3 times as long as A and C together to do the work. In how many days can B alone do the work?
Correct Answer

(B) 40 days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{left( {A + C}
ight)}&:&B \
{{ ext{Time}}}&1&{}&3 \
{{ ext{Efficiency}}}&3&{}&1
end{array}] $$B,{ ext{alone}} = frac{{10 imes 4}}{1} = 40,{ ext{days}}$$

[#125] A can do 20% of work in 4 days, B can do $$33frac{1}{3}\% $$ xa0of the same work in 10 days. They worked together for 9 days. C completed the remaining work in 6 days. B and C together complete 75% of the same work in:
Correct Answer

(C) 10 days

Explanation

Solution: A = 20 days B = 30 days (A + B) × 9 + C × 6 = 60 (3 + 2) × 9 + C × 6 = 60 C = $$frac{5}{2}$$ unit C = $$frac{{60 imes 2}}{5}$$ xa0= 24 days (B + C) × x = 60 × $$frac{3}{4}$$ $$left( {2 + frac{5}{2}}
ight){ ext{x}} = 45$$ 9x = 90 x = 10 days