Time And Work - Study Mode

[#16] A labourer was appointed by a contractor on the condition he would be paid Rs. 75 for each day of his work but would be, fined at the rate of Rs. 15 per day for his absent. After 20 days, the contractor paid the labourer Rs. 1140. The number of days the labourer absented from work was ?
Correct Answer

(C) 4 days

Explanation

Solution: If labourer had come for 20 days he would have earned = 20 × 75 = Rs. 1500 If labourer had absented for 20 days he would have earned fined for = 20 × 15 = Rs. 300

[#17] 18 men can complete a piece of work in 63 days. 9 women take 189 days to complete the same piece of work. How many days will 4 men, 9 women and 12 children together take to complete the piece of work if 7 children alone can complete the piece of work in 486 days ?
Correct Answer

(D) 81 days

Explanation

Solution: $$eqalign{
& { ext{1 men's 1 day's work}} cr
& = frac{1}{{63 imes 18}} cr
& = frac{1}{{1134}} cr
& { ext{1 women's 1 day's work}} cr
& = frac{1}{{189 imes 9}} cr
& = frac{1}{{1701}} cr
& { ext{1 children's 1 day's work}} cr
& = frac{1}{{486 imes 7}} cr
& = frac{1}{{3402}} cr} $$ (4 men + 9 women + 12 children)'s 1 day's work $$eqalign{
& = frac{4}{{1134}} + frac{9}{{1701}} + frac{{12}}{{3402}} cr
& = frac{{42}}{{3402}} cr
& = frac{1}{{81}} cr} $$ Hence, 4 mens , 9 women and 12 children together will complete the work in 81 days.

[#18] 16 men can finish a work in 24 days and 48 boys can finish the same work in 16 days. 12 men started the work and after 4 days 12 boys joined them. In how many days can they finish the remaining work ?
Correct Answer

(D) None of these

Explanation

Solution: $$eqalign{
& { ext{1 men's 1 day's work}} cr
& = frac{1}{{24 imes 16}} cr
& = frac{1}{{384}} cr
& { ext{1 boy's 1 day's work}} cr
& = frac{1}{{16 imes 48}} cr
& = frac{1}{{768}} cr
& { ext{12 men's 4 day's work}} cr
& = left( {frac{{12}}{{384}} imes 4}
ight) cr
& = frac{1}{8} cr
& { ext{Remaining work}} cr
& = left( {1 - frac{1}{8}}
ight) cr
& = frac{7}{8} cr
& left( {{ ext{12 men}} + { ext{12 boy}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{{12}}{{384}} + frac{{12}}{{768}}}
ight) cr
& = left( {frac{1}{{32}} + frac{1}{{64}}}
ight) cr
& = frac{3}{{64}} cr} $$ $$frac{3}{{64}}$$ work is done by (12 men + 12 boy)'s in 1 day $$eqalign{
& herefore frac{7}{8}{ ext{ work is done by them in }} cr
& { ext{ = }}frac{{64}}{3} imes frac{7}{8}{ ext{ days}} cr
& = frac{{56}}{3}{ ext{ days}} cr
& = { ext{18}}frac{2}{3}{ ext{ days}} cr} $$

[#19] 4 men and 10 women were put on a work. They completed $$frac{1}{3}$$ of the work in 4 days. After this 2 men and 2 women were increased. They completed $$frac{2}{9}$$ more of the work in 2 days. If the remaining work is to be completed in 3 days, then how many more women must be increased ?
Correct Answer

(A) 8

Explanation

Solution: $$eqalign{
& { ext{Let 1 man's 1 day's work}} = x cr
& { ext{And }} cr
& { ext{1 women's 1 day's work}} = y cr
& { ext{Then,}} cr
& Rightarrow 4x + 10y = frac{1}{3} imes frac{1}{4} = frac{1}{{12}} cr
& Rightarrow 4x + 10y = frac{1}{{12}} cr
& Rightarrow 2x + 5y = frac{1}{{24}}.....(i) cr
& { ext{And,}} cr
& Rightarrow 6x + 12y = frac{1}{9} cr
& Rightarrow 2x + 4y = frac{1}{{27}}.....({ ext{ii}}) cr} $$ Subtracting (ii) from (i), we get $$eqalign{
& y = frac{1}{{24}} - frac{1}{{27}} = frac{1}{{216}} cr
& { ext{Now,}} cr} $$ Now, (6 men + 12 women)'s 3 day's work $$eqalign{
& = left( {frac{1}{9} imes 3}
ight) cr
& = frac{1}{3} cr
& { ext{Work completed}} cr
& = left( {frac{1}{3} + frac{2}{9} + frac{1}{3}}
ight) cr
& = frac{8}{9} cr
& herefore { ext{Remainig work}} cr
& = left( {1 - frac{8}{9}}
ight) cr
& = frac{1}{9} cr
& { ext{1 women's 3 day's work}} cr
& = left( {frac{1}{{216}} imes 3}
ight) cr
& = frac{1}{{72}} cr} $$ In 3 day's $$frac{1}{{72}}$$ work is done by 1 women. $$eqalign{
& herefore { ext{In 3 day's }}frac{1}{9}{ ext{work is done by}} cr
& { ext{ = }}left( {72 imes frac{1}{9}}
ight) cr
& = { ext{8 women}}{ ext{.}} cr} $$

[#20] A can do a piece of work in 5 days less than the time taken by B to do it. If both of them together take $${ ext{11}}frac{1}{9}$$ days, then the time taken by B alone to do the same work (in days ) is ?
Correct Answer

(C) 25 days

Explanation

Solution: Try these question with the help of the option to save the time Let B takes x days to complete the work ∴ A takes (x - 5)days Now take the option 'B' i.e x = 20days ∴ Time taken by B = 20days and A = 15days T.W = LCM of number of day taken by A and B = 60. Work Efficiency ration A : B = 4 : 3 ∴Total Time taken to complete the work together = $$frac{60}{4+3}$$ = xa0 $$8frac{4}{7}$$ xa0days This option not matched with $${ ext{11}}frac{1}{9}$$ Now take the option 'C' i.e x = 25days ∴ Time taken by B = 25days and A = 20days T.W = LCM of number of day taken by A and B = 100. Work Efficiency ration A : B = 5 : 4 ∴Total Time taken to complete the work together = $$frac{100}{5+4}$$ = xa0 $$11frac{1}{9}$$ xa0days Hence , Option (C) is the correct .