Time And Work - Study Mode

[#156] A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it ?
Correct Answer

(C) 12 hours

Explanation

Solution: $$eqalign{
& { ext{A's 1 hour's work}} = frac{1}{4} cr
& left( {{ ext{B}} + { ext{C}}}
ight){ ext{'s 1 hour's work}} = frac{1}{3} cr
& left( {{ ext{A}} + { ext{C}}}
ight){ ext{'s 1 hour's work}} = frac{1}{2} cr
& left( {{ ext{A}} + { ext{B}} + { ext{C}}}
ight){ ext{'s 1 hour's work}} cr
& = frac{1}{4} + frac{1}{3} cr
& = frac{7}{{12}} cr
& herefore { ext{B's 1 hour's work}} cr} $$ = (A + B + C)'s 1 hour's work - (A + C)'s 1 hour's work $$eqalign{
& = frac{7}{{12}} - frac{1}{2} cr
& = frac{1}{{12}} cr} $$ So, B alone can complete the work in 12 hours.

[#157] Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Correct Answer

(C) 8 hours 15 minutes

Explanation

Solution: $$eqalign{
& { ext{Number}},{ ext{of}},{ ext{pages}},{ ext{typed}},{ ext{by}},{ ext{Ravi}},{ ext{in}},{ ext{1}},{ ext{hour}} cr
& = frac{{32}}{6} = frac{{16}}{3} cr
& { ext{Number}},{ ext{of}},{ ext{pages}},{ ext{typed}},{ ext{by}},{ ext{Kumar}},{ ext{in}},{ ext{1}},{ ext{hour}} cr
& = frac{{40}}{5} = 8 cr
& { ext{Number}},{ ext{of}},{ ext{pages}},{ ext{typed}},{ ext{by}},{ ext{both}},{ ext{in}},{ ext{1}},{ ext{hour}} cr
& = {frac{{16}}{3} + 8} = frac{{40}}{3} cr
& herefore { ext{Time}},{ ext{taken}},{ ext{by}},{ ext{both}},{ ext{to}},{ ext{type}},{ ext{110}},{ ext{pages}} cr
& = {110 imes frac{3}{{40}}} { ext{hours}} cr
& = 8frac{1}{4},{ ext{hours}},{ ext{(or)}},{ ext{8}},{ ext{hours}},{ ext{15}},{ ext{minutes}} cr} $$

[#158] A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
Correct Answer

(C) $$3frac{3}{7}$$xa0 days

Explanation

Solution: Formula: If A can do a piece of work in n days, then A's 1 day's work = $$frac{1}{{ ext{n}}}$$ $$eqalign{
& (A + B + C)'s,1,{ ext{day's work}} cr
& = {frac{1}{{24}} + frac{1}{6} + frac{1}{{12}}} = frac{7}{{24}} cr} $$ Formula: If A's 1 day's work = $$frac{1}{{ ext{n}}}$$ , then A can finish the work in n days So, all the three together will complete the job in $$ {frac{{24}}{7}} { ext{ days}} = 3frac{3}{7}{ ext{ days}}$$

[#159] Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Correct Answer

(B) 16

Explanation

Solution: Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 Suppose Tanya takes x days to do the work 5 : 4 :: 20 : x ⇒ $$x = {frac{{4 imes 20}}{5}} $$ ⇒ x = 16 days Hence, Tanya takes 16 days to complete the work

[#160] A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
Correct Answer

(B) 6 days

Explanation

Solution: $$eqalign{
& { ext{Suppose}},{ ext{A,}},{ ext{B}},{ ext{and}},{ ext{C}},{ ext{take}} cr
& x,,frac{x}{2},,frac{x}{3},{ ext{days}},{ ext{respectively}},{ ext{to}},{ ext{finish}},{ ext{the}},{ ext{work}} cr
& { ext{Then}},, {frac{1}{x} + frac{2}{x} + frac{3}{x}} = frac{1}{2} cr
& Rightarrow frac{6}{x} = frac{1}{2} cr
& Rightarrow x = 12 cr
& { ext{So,}},{ ext{B}},{ ext{takes}}, {frac{{12}}{2}} cr
& = 6,{ ext{days}},{ ext{to}},{ ext{finish}},{ ext{the}},{ ext{work}} cr} $$