Time And Work - Study Mode

[#111] A can do piece of work in 15 days. B is 25% more efficient than A, and C is 40% more efficient than B, A and C work together for 3 days and then C leaves. A and B together will complete the remaining work in:
Correct Answer

(A) 3 days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&x08egin{gathered}
{ ext{A}},,,,,,{ ext{B}},,,,,,{ ext{C}} hfill \
{ ext{4}},,,{ ext{:}},,,{ ext{5}},,,{ ext{:}},,,{ ext{7}} hfill \
{ ext{5}},,,{ ext{:}},,,{ ext{7}},,,,,,,,,, hfill \
end{gathered} \
{{ ext{Efficiency}} o }&{overline {,4,:,5,:,7,} }
end{array}] Total work = 4 × 15 = 60 units (A + C) × 3 + (A + B)x = 60 11 × 3 + 9 × x = 60 33 + 9x = 60 9x = 27 x = 3 days

[#112] A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find the how many days B alone can do the work?
Correct Answer

(A) 90 days

Explanation

Solution: A : C = 2 : 1 A = 4 unit C = 2 unit B = 1 unit B = $$frac{{90}}{1}$$ = 90 days

[#113] To do a certain work, the ratio of the efficiencies of A and B is 7 : 5. Working together, they can complete the same work in $$17frac{1}{2}$$xa0days. A alone will complete 60% of the same work in:
Correct Answer

(A) 18 days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{ ext{A}}&:&{ ext{B}} \
{{ ext{Efficiency}}}&7&:&5
end{array}] $$eqalign{
& { ext{A}} + { ext{B}} = 12 imes frac{{35}}{2} = 35 imes 6{ ext{ Total work}} cr
& { ext{A}} = frac{{35 imes 6 imes frac{3}{5}}}{7} = 18{ ext{ days}} cr} $$

[#114] A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in:
Correct Answer

(C) 110 Days

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&A&:&{B + C}&{}&{} \
{{ ext{Efficiency}} o }&{{1_{ imes 4}}}&:&{{1_{ imes 4}}}& Rightarrow &{{2_{ imes 4}}} \
{}&{A + B}&:&C&{}&{} \
{{ ext{Days}} o }&{36}&:&{60}&{}&{} \
{{ ext{Efficiency}} o }&5&:&3& Rightarrow &8 \
{{ ext{Efficiency}} o }&A&:&B&:&C \
{}&4&:&1&:&3
end{array}] $$eqalign{
& { ext{Total work}} = 3 imes 60 = 180 cr
& left( {A + C}
ight) imes 10 + B imes x = 180 cr
& 7 imes 10 + 1 imes x = 180 cr
& x = 110{ ext{ Days}} cr} $$

[#115] A, B and C can complete a piece of work separately in 10, 20 and 40 days, respectively. In how many days will the work be completed if A is assisted by both B and C every third day?
Correct Answer

(A) $$8frac{2}{7}$$

Explanation

Solution: A's three days work = 4 × 3 = 12 B and C one day work = 3 × 1 = 3 A, B, C three days work = 15 unit A, B, C six days work = 30 unit 7 th day work = 4 unit 8 th day work = 4 unit Total = 38 unit Work left 2 unit 7 units in 1 days 2 units in $$frac{2}{7}$$ days Total time = $$8frac{2}{7}$$ days