Time And Work - Study Mode

[#76] If the work done by (x - 1) men in (x + 1) days and the work done by (x + 2) men in (x - 1) days are in the ratio 9 : 10, then the value of x is equal to ?
Correct Answer

(D) 8

Explanation

Solution: Put values in formula $$frac{{{{left( {x - 1}
ight)}_{{ ext{men}}}} imes {{left( {x + 1}
ight)}_{{ ext{days}}}}}}{{{{ ext{9}}_{{ ext{work}}}}}} = $$ xa0 xa0 xa0 $$frac{{{{left( {x + 2}
ight)}_{{ ext{men}}}} imes {{left( {x - 1}
ight)}_{{ ext{days}}}}}}{{{{10}_{{ ext{work}}}}}}$$ $$eqalign{
& Rightarrow frac{{x + 1}}{9} = frac{{x + 2}}{{10}} cr
& Rightarrow 10x + 10 = 9x + 18 cr
& Rightarrow x = 8 cr} $$

[#77] A can do a piece of work in 70 days and B is 40% more efficient then A. Then the number of days taken by B to do the same work is = ?
Correct Answer

(C) 50 days

Explanation

Solution: A : B Efficiency → 100% : 140% 5 : 7 ⤩ Time 7 : 5 ×10↓ ↓×10 Actual Time 70 days 50 days

[#78] A can do a certain work in 12 days. B is 60% more efficient then A. How many days will B and A together take to do the same job?
Correct Answer

(D) $$frac{{60}}{{13}}{ ext{days}}$$

Explanation

Solution: Time taken by B to complete the work $$eqalign{
& = 12 imes frac{{100}}{{160}} cr
& = frac{{15}}{2},{ ext{days}} cr} $$ ∴ (A + B)'s 1 day's work $$eqalign{
& = frac{1}{{12}} + frac{2}{{15}} cr
& = frac{{5 + 8}}{{60}} cr
& = frac{{13}}{{60}} cr} $$ Hence, the work will be completed in $$frac{{60}}{{13}}$$ days Alternate: Ratio of time, taken by A and B = 160 : 100 = 8 : 5 If A takes 8 days, B takes 5 days. If A takes 12 days, B takes = $$frac{5}{8} imes 12 = frac{{ 15}}{2}$$ Time take by A = 12 days Time take by B = 7.5 days L.C.M. of Total Work = 60 Ratio of time, taken by A and B = 8 : 5 Time taken by A and B together to complete the task $$ = frac{{60}}{{13}}{ ext{days}}$$

[#79] A, B and C completed a work costing Rs. 1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A ?
Correct Answer

(A) Rs. 600

Explanation

Solution: Let the daily wages of A, B and C be Rs. 5x, Rs. 6x and Rs. 4x respectively. Then, ratio of their amounts $$eqalign{
& = left( {5x imes 6}
ight):left( {6x imes 4}
ight):left( {4x:9}
ight) cr
& = 30:24:36 cr
& = 5:4:6 cr
& herefore { ext{A's amount}} cr
& = { ext{Rs}}{ ext{.}}left( {1800 imes frac{5}{{15}}}
ight) cr
& = { ext{Rs}}{ ext{.600}} cr} $$

[#80] P and Q together can do a job in 6 days. Q and R can finish the same job in $$frac{{60}}{7}$$ days. P started the work and worked for 3 days. Q and R continued for 6 days to finish the work. Then the difference of days in which R and P can complete the alone is P can complete the job alone is ?
Correct Answer

(A) 10 days

Explanation

Solution: L.C.M. of Total Work = 60 One day work of P + Q = $$frac{{60}}{{6}}$$ = 10 unit/day efficiency One day work of Q + R = $$frac{{60}}{{frac{{60}}{7}}}$$ = 7 unit/day efficiency $$eqalign{
& left( {{ ext{Q}} + { ext{R}}}
ight){ ext{ 6 days work}} cr
& = 7 imes 6 cr
& = 42{ ext{ units}} cr} $$ Then in 3 days = total work = 18 $$eqalign{
& { ext{P completes}} cr
& = 60 - 42 cr
& = 18{ ext{ units}} cr
& { ext{P's efficiency}} cr
& = frac{{18}}{3} cr
& = 6{ ext{ units/day}} cr
& { ext{Q's efficiency}} cr
& = 10 - 6 cr
& = 4{ ext{ units/day}} cr
& { ext{R's efficiency}} cr
& = 7 - 4 cr
& = 3{ ext{ units/day}} cr
& { ext{P completes whole work in}} cr
& = frac{{60}}{6} cr
& = { ext{10 days}} cr
& { ext{R completes whole work in}} cr
& = frac{{60}}{3} cr
& = { ext{20 days}} cr
& { ext{Difference is}} cr
& = left( {20 - 10}
ight) cr
& = 10{ ext{ days }} cr} $$