Time And Work - Study Mode

[#201] 25 persons can complete a work in 60 days. They started the work. 10 persons left the work after x days. If the whole work was completed in 80 days, then what is the value of x?
Correct Answer

(C) 30

Explanation

Solution: Total work = 25 × 60 = 1500 x × 25 + (80 - x) × 15 = 1500 25x - 15x + 1200 = 1500 10x = 300 x = 30

[#202] Ten men begin to do a work. But after some days, four of them left the job. As a result, the job that could have been completed in 40 days is completed in 50 days. How many days after the commencement of the work did the four men leave?
Correct Answer

(D) 25

Explanation

Solution: Let after x day 4 men left the work 10 × x + 6 × (50 - x) = 10 × 40 10x + 300 - 6x = 400 4x = 400 - 300 4x = 100 x = 25

[#203] X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in:
Correct Answer

(B) 36 days

Explanation

Solution: According to the question, X → 24 days ⇒ Work done by X in 4 days alone = 4 × 1 = 4 units ⇒ Remaining work = 24 - 4 = 20 units ⇒ 20 units done by both together in (16 - 4 days) = 12 days ⇒ Then efficiencies of (X + Y) $$ = frac{{{ ext{work}}}}{{{ ext{days}}}} = frac{{20}}{{12}} = frac{5}{3} = 1 + frac{2}{3}$$ ⇒ Efficiency of Y = $$frac{2}{3}$$ ⇒ Time taken by Y alone to complete the total work $$ = frac{{24}}{{frac{2}{3}}} = 36{ ext{ days}}$$ Alternate solution: $$eqalign{
& X imes 20 = left( {X + Y}
ight) imes 12 cr
& frac{X}{{X + Y}} = frac{{12}}{{20}} cr
& = frac{{3 o { ext{Efficiency of }}X}}{{5 o { ext{Efficiency of }}left( {X + Y}
ight)}} cr} $$ Efficiency of Y = 5 - 3 = 2 units/day Total work = 24 × 3 = 72 units Total time taken by Y = $$frac{{72}}{2}$$ = 36 days

[#204] To do a certain work, A and B work on alternate days, with B beginning the work on the first day. A can finish the work alone in 48 days. If the work gets completed in $$11frac{1}{3}$$xa0days, then B alone can finish 4 times the same work in:
Correct Answer

(C) 27 days

Explanation

Solution: Let total work = 48 unit B × 6 + A × $$frac{{16}}{3}$$ = 48 B × 6 + 1 × $$frac{{16}}{3}$$ = 48 B × 6 = $$frac{{128}}{3}$$ B = $$frac{{64}}{9}$$ 4 × Total work = B × Days Now, 48 × 4 = $$frac{{64}}{9}$$ × Days 27 = Days

[#205] A is twice as good a workman as B and together they finish a piece of work in 22 days. In how many days will A alone finish the same work?
Correct Answer

(D) 33 days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&A&B \
{{ ext{Efficiency}}}&2&1
end{array}] $$eqalign{
& { ext{Total work}} = 3 imes 22 = 66 cr
& A o frac{{66}}{2} = 33{ ext{ days}} cr} $$