Time And Work - Study Mode

[#116] A tyre has 3 punctures. The first puncture alone would have made the tyre flat in 9 minutes, the second alone would have done it in 18 minutes, the third alone would have done it in 6 minutes. If the air leaks out at a constant rate, then how long (in minutes) does it take for all the punctures together to make it flat?
Correct Answer

(D) 3

Explanation

Solution: $$ herefore frac{{18}}{{2 + 1 + 3}} = 3{ ext{ minutes}}$$

[#117] Ramesh and Rahman can do a work in 20 and 25 days respectively. After doing collectively 10 days of work, they leave the work due to illness and Suresh completes rest of the work in 3 days. How many days Suresh alone can take to complete the whole work ?
Correct Answer

(D) 30 days

Explanation

Solution: (Ramesh & Rahman)'s 1 day's work $$ = frac{1}{{20}} + frac{1}{{25}} = frac{{5 + 4}}{{100}} = frac{9}{{100}}$$ ∴ Their 10 day's work $$ = frac{{90}}{{100}} = frac{9}{{10}}$$ ∴ Remaining work $$ = 1 - frac{9}{{10}} = frac{1}{{10}}$$ ∵ Suresh does $$frac{1}{{10}}$$ work in 3 days ∴ Time taken by Suresh in doing 1 work = 3 × 10 = 30 days

[#118] The ratio of the amount of work done by (x - 1) labours in (x + 1) days and (x + 1) labours in (x + 2) days is 5 : 6. Then the value of x is ?
Correct Answer

(A) 16

Explanation

Solution: $$eqalign{
& { ext{From }}{{ ext{M}}_1}{{ ext{D}}_1} = {{ ext{M}}_2}{{ ext{D}}_2} cr
& Rightarrow frac{{{{ ext{M}}_1}{{ ext{D}}_1}}}{{{{ ext{M}}_2}{{ ext{D}}_2}}} = frac{5}{6} cr
& Rightarrow frac{{left( {x - 1}
ight)left( {x + 1}
ight)}}{{left( {x + 1}
ight)left( {x + 2}
ight)}} = frac{5}{6} cr
& Rightarrow frac{{left( {x - 1}
ight)}}{{left( {x + 2}
ight)}} = frac{5}{6} cr
& Rightarrow 6x - 6 = 5x + 10 cr
& Rightarrow x = 16 cr} $$

[#119] A can do a work in 36 days, B in 18 days and C in 12 days. Every 2nd day B and every 3rd day C, helps A .Then in how many days the work will be completed?
Correct Answer

(B) 14

Explanation

Solution: Let to work Total Work = 36 One day work of A = $$frac{{36}}{{36}}$$ = 1 unit/day One day work of B = $$frac{{36}}{{18}}$$ = 2 unit/day One day work of C = $$frac{{36}}{{12}}$$ = 3 unit/day In 3 days cycle total work done is A, A + B, A + C = 1 + (1 + 2) + (1 + 3) = 8 unit/Cycle ∴ 32 units of the work completed in 4 cycle and reminder 4 units of works in next two days. 1 cycle = 3 days ∴ 4 cycle = 12 days And remaining 4 unit work done in next two days. In days 13, A will work 1 unit and in day 14, A and B will work 3 units . Total number the day required to complete the work in the given condition is 14 days

[#120] A can complete 25% of a work in 15 days. He works for 15 days and then B alone finishes the remaining work in 30 days. In how many days will A and B working together finish 50% of the same work?
Correct Answer

(C) 12

Explanation

Solution: $$frac{{250}}{{100}}A o 15{ ext{ days}}$$ A → 60 days. (Whole work) Let A do 60 work in 60 days. A do 15 day work, remaining work completed by A in 45 days. But B do in 30 days. ∴ 45A = 30B $$frac{{ ext{A}}}{{ ext{B}}} = frac{2}{3},,,left( {{ ext{efficiency}}}
ight)$$ A + B = 5 Total work = A × 60 = 2 × 60 = 120 50% of 120 = 60 A + B = $$frac{{60}}{5}$$ = 12