Time And Work - Study Mode

[#271] To complete a piece of work A and B take 8 days, B and C 12 days. A, B and C take 6 days. A and C will take :
Correct Answer

(C) 8 Days

Explanation

Solution: Given (A+B)'s one day's work = $$frac{1}{8}$$ (B + C)'s one day's work = $$frac{1}{{12}}$$ (A + B + C) 's 1 day's work = $$frac{1}{6}$$ Work done by A, alone= (A + B + C) 's 1 day's work - (B + C)'s one day's work $$ = frac{1}{6} - frac{1}{{12}} = frac{{2 - 1}}{{12}} = frac{1}{{12}}$$ Work done by C, alone = (A + B + C) 's 1 day's work - (A + B)'s one day’s work $$ = frac{1}{6} - frac{1}{8} = frac{{4 - 3}}{{24}} = frac{1}{{24}}$$ ⇒ (A + C)’s one day’s work $$eqalign{
& = frac{1}{{12}} + frac{1}{{24}} cr
& = frac{{2 + 1}}{{24}} cr
& = frac{3}{{24}} = frac{1}{8} cr} $$ ⇒ (A + C) will take 8 days to complete the work together

[#272] Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the cistern will be filled in:
Correct Answer

(A) 7.5 hr

Explanation

Solution: Work done by all the tanks working together in 1 hour,
$$ Rightarrow frac{1}{{10}} + frac{1}{{12}} - frac{1}{{20}} = frac{2}{{15}}$$ Hence, tank will be filled in $$frac{{15}}{2}$$ = 7.5 hour.

[#273] Three taps A, B and C together can fill an empty cistern in 10 minutes. The tap A alone can fill it in 30 minutes and the tap B alone in 40 minutes. How long will the tap C alone take to fill it?
Correct Answer

(B) 24 minutes

Explanation

Solution: A, B and C together can fill 100% empty tank in 10 minutes Work rate of (A + B + C) = $$frac{{100}}{{10}}$$ = 10% per minute A alone can fill the tank in 30 minutes Work rate of A = $$frac{{100}}{{30}}$$ = 3.33% per minute B alone can fill the tank in 40 minutes Work rate of B = $$frac{{100}}{{40}}$$ = 2.5% Work rate of (A + B) = 3.33 + 2.5 = 5.83% per minute Work rate of C, = Work rate of (A + B + C) - (A + B) = 10 - 5.83 = 4.17% per minute So, C takes = $$frac{{100}}{{4.17}}$$ ≈ 24 minutes to fill the tank

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

(C) 11 days

Explanation

Solution: Work rate of A = $$frac{{100}}{9}$$ = 11.11% work per day Work rate of B = $$frac{{100}}{{15}}$$ = 6.66% work per day They together can do (A + B) = 11.11 + 6.66 ≈ 18% work per day They are working in alternate day, so we take 2 days = 1 unit of day Therefore, in one unit of day they can complete 18% of work (A + B) can complete 90% of work in 5 units of days. i.e. (5 × 18) And the rest 10% work will be completed by A in Next day So, total number of day, = 5 Unit of days + 1 day of A = 2 × 5 + 1 = 11 days

[#275] Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. Another pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is also opened. The tank filled up in:
Correct Answer

(B) 46 min

Explanation

Solution: Pipe A can fill empty tank in 36 min. Pipe A can fill the tank = $$frac{{100}}{{36}}$$ = 2.77% per minute Pipe B can fill empty tank in 45 min. Pipe B can fill the tank = $$frac{{100}}{{45}}$$ = 2.22% per min. A and B can together fill the tank = (2.77 + 2.22) ≈ 5% per minute So, A and B can fill the tank in 7 min. = 7 × 5 = 35% of the tank Rest tank to be filled = 100 - 35 = 65% C can empty the full tank in 30 min. C can empty the tank = $$frac{{100}}{{30}}$$ = 3.33% per min. C is doing negative work i.e. emptying the tank A, B and C can together fill the tank, = 2.77% + 2.22% - 3.33% = 1.67% tank per minute So, A, B and C will take time to fill 65% empty tank, = $$frac{{65}}{{1.67}}$$ = 39 min. (Approx)