Time And Work - Study Mode

[#171] A man is twice as fast as a women and a woman is twice as fast as a boy in doing a work. If all of them, a man , a woman and a boy can finish the work in 7 days, a boy will do it alone ?
Correct Answer

(A) 49 days

Explanation

Solution: Man : Woman : Boy Efficiency 4 : 2 : 1 Total work = Time × (Efficiency of man + woman + boy) ⇒ 7 days × (4 + 2 + 1) = 49 units ∴ Boy can do this work in = $$frac{{49}}{1}$$ = 49 days

[#172] A's 2 days work is equal to B's 3 days work. If A can complete the work in 8 days, then to complete the work B will take ?
Correct Answer

(B) 12 days

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& Rightarrow 2{ ext{A}} = { ext{3B}} cr
& Rightarrow frac{{ ext{A}}}{{ ext{B}}} = frac{3}{2} cr
& Rightarrow { ext{Then efficiency ratio }} cr
& { ext{A}}:{ ext{B}} = 3:2 cr} $$ ⇒ We know that time is inversely proportional to efficiency ⇒ Then time taken by them in ratio $$eqalign{
& { ext{A}}:{ ext{B}} = mathop {mathop {{ ext{ }}2}limits_{4 imes downarrow } { ext{ }}}limits_{8{ ext{days}}} :mathop {mathop 3limits_{{ ext{ }} downarrow imes 4} }limits_{12{ ext{days}}} cr
& x08ecause { ext{A can do the work in 8 days}} cr
& Rightarrow { ext{i}}{ ext{.e, 2 units}} o { ext{8}} cr
& ,,,,,,,,,,,,,,,,,{ ext{1 unit}} o { ext{4}} cr
& Rightarrow { ext{Time taken by B}} o { ext{3 units}} cr
& = 3 imes 4 cr
& = 12{ ext{ days}} cr} $$

[#173] If A, B and C can complete a piece of work in 6 days. If A can work twice faster than B and thrice faster then C, than the number of days C alone can complete the work is ?
Correct Answer

(B) 33 days

Explanation

Solution: A + B + C = 6 days [6 days total work] $$eqalign{
& { ext{According to the question,}} cr
& { ext{Ratio of their efficiencies,}} cr
& { ext{A}}:{ ext{B}}:{ ext{C}} cr
& 6{ ext{ }}:3{ ext{ }}:2 cr
& { ext{Total efficiencies}} cr
& left( {6 + 3 + 2}
ight){ ext{units}} = 11{ ext{ units}} cr
& { ext{Total work}} = 11 imes 6 = 66{ ext{ units}} cr} $$ Therefore, time taken by C to complete the work $$frac{{{ ext{Total work}}}}{{{ ext{Efficiencies}}}} = frac{{66}}{2} = 33{ ext{ days}}$$

[#174] A can do half of a piece of work in 1 day,where B can do full. B can do half the work as C in 1 day. The ratio of their efficiencies of work is = ?
Correct Answer

(A) 1 : 2 : 4

Explanation

Solution: A : B = 1 : 2 B : C = 1 : 2 (Multiply by 2) B : C = 2 : 4 A : B : C = 1 : 2 : 4

[#175] If 3 men or 9 boys can finish a piece of work in 21 days, in how many days can 5 men and 6 boys together do the same piece of work ?
Correct Answer

8 days

Explanation

Solution: $$eqalign{
& { ext{1 men's 1 day's work}} cr
& = frac{1}{{21 imes 3}} cr
& = frac{1}{{63}} cr
& { ext{1 boy's 1 day's work}} cr
& = frac{1}{{21 imes 9}} cr
& = frac{1}{{189}} cr
& left( {{ ext{5 men}} + { ext{6 boy}}}
ight){ ext{'s 1 day's work}} cr
& = frac{5}{{63}} + frac{6}{{189}} cr
& = frac{5}{{63}} + frac{2}{{63}} cr
& = frac{7}{{63}} cr
& = frac{1}{9} cr} $$ Hence, 5 men's and 6 boy's together can do the work in 9 days.