Time And Work - Study Mode

[#181] A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?
Correct Answer

(D) 48 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 1 day's work}} = frac{1}{{12}} cr
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} = frac{1}{8} cr
& left( {{ ext{A}} + { ext{C}}}
ight){ ext{'s 1 day's work}} = frac{1}{{62}} cr} $$ [ (A + B)'s 1 day's work + (B + C)'s 1 day's work ] - (A + C)'s 1 day's work $$eqalign{
& = frac{1}{{12}} + frac{1}{8} - frac{1}{6} cr
& Rightarrow 2left( {{ ext{B's 1 day's work}}}
ight) = frac{1}{{24}} cr
& Rightarrow { ext{B's 1 day's work}} = frac{1}{{48}} cr} $$ Hence, B alone can do the work in 48 days.

[#182] A can build a wall in the same time in which B and C together can do it. If A and B together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it ?
Correct Answer

(C) 175 days

Explanation

Solution: $$eqalign{
& left( {{ ext{A}} + { ext{B}}}
ight){ ext{'s 1 day's work}} = frac{1}{{25}} cr
& { ext{C's 1 day's work}} = frac{1}{{35}} cr
& left( {{ ext{A}} + { ext{B}} + { ext{C}}}
ight){ ext{'s 1 day's work}} cr
& = left( {frac{1}{{25}} + frac{1}{{35}}}
ight) cr
& = frac{{12}}{{175}}.....({ ext{i}}) cr} $$ Also, A's 1 day's work = (B + C)'s 1 day's work.....(ii) $$eqalign{
& { ext{From (i) and (ii), we get : }} cr
& Rightarrow { ext{2}} imes left( {{ ext{A's 1 day's work}}}
ight) = frac{{12}}{{175}} cr
& Rightarrow { ext{A's 1 day's work}} = frac{6}{{175}} cr
& herefore { ext{B's 1 day's work}} cr
& = left( {frac{1}{{25}} - frac{6}{{175}}}
ight) cr
& = frac{1}{{175}} cr} $$

[#183] Madhu takes twice as much time as Uma to complete a work and Rahul does it in the same time as Madhu and Uma together. If all three working together can finish the work in 6 days, then the time taken by Madhu to finish the work is = ?
Correct Answer

(C) 36 days

Explanation

Solution: Suppose Uma takes x days to complete a work Then, Madhu takes 2x days to complete the work Uma's 1 day's work = $$frac{1}{x}$$ Madhu's 1 day's work = $$frac{1}{{2x}}$$ Rahul's 1 day's work = (Madhu + Uma)'s 1 day's work $$eqalign{
& = frac{1}{{2x}} + frac{1}{x} cr
& = frac{3}{{3x}}{ ext{ }} cr} $$ (Madhu + Uma + Rahul)'s 1 day's work $$eqalign{
& = frac{3}{{3x}} + frac{1}{{2x}} + frac{1}{x} = frac{6}{{3x}} = frac{3}{x} cr
& herefore frac{3}{x} = frac{1}{6} cr
& Rightarrow x = 18{ ext{ }} cr} $$ Hence, Madhu takes (2 × 18) = 36 days to complete the work

[#184] If 28 men complete $$frac{7}{8}$$ of a piece of work in a week, then the number of men, who must be engaged to get the remaining work completed in another week, is = ?
Correct Answer

(C) 4

Explanation

Solution: $$eqalign{
& frac{{{ ext{28 M}} imes { ext{1 Week}}}}{{frac{7}{8}}} = frac{{x imes { ext{ 1 Week}}}}{{frac{1}{8}}} cr
& Leftrightarrow x = 4{ ext{ men}} cr} $$

[#185] The charges per hour of internet surfing is increased by 25% then find the percentage decrease in the time period of surfing user (a net savy) who can afford only 10% increase in expenditure:
Correct Answer

(B) 12%

Explanation

Solution: Time × Rate = total charges
100 × 100 = 10000 X × 125 = 110 [25% increase in rate, user can afford only 10% increase] X = $$frac{{110}}{{125}} imes 100$$ xa0 = 88% Thus, decrease in time = 12%