Time And Work - Study Mode

[#221] A can complete work in 25 days and B can complete the same work in 20 days. They started the work together but B left after 4 days and A continued to work. In how many days will the entire work be completed?
Correct Answer

(B) 20

Explanation

Solution: Total work of (A + B) in 4 days = 4(4 + 5) = 36 Remaining work = 100 - 36 = 64 A = $$frac{{64}}{4}$$ = 16 days Total days = 4 + 16 = 20 days

[#222] P and Q together can do a work in 12 days. P alone can do the same work in 36 days. In how many days can Q alone complete two-third part of the same work?
Correct Answer

(A) 12

Explanation

Solution: Efficiency of Q = 2 So, required answer = $$frac{{36 imes frac{2}{3}}}{2}$$ xa0= 12 days

[#223] A can finish a piece of work in a certain number of days. B takes 45% more number of days to finish the same work independently. They worked together for 58 days and then the remaining work was done by B alone in 29 days. In how many days could A have completed the work, had he worked alone?
Correct Answer

(B) 118 days

Explanation

Solution: $$eqalign{
& 45\% = frac{9}{{20}} cr
& { ext{Efficiency A}} = 29{ ext{ and B}} = 20 cr
& 58 imes 49 + 29 imes 20 = 3422 cr
& { ext{Required answer A}} = frac{{3422}}{{29}} = 118,{ ext{days}} cr} $$

[#224] 20 man can finish a work in 30 days. They started working, but 4 men left the work after 10 days. In how many days would the work be completed?
Correct Answer

(C) 35

Explanation

Solution: Total work = 30 × 20 = 600 After 10 days = 20 × 10 = 200 Remaining work = 600 - 200 = 400 4 men left, remaining = 16 men 16 × D = 400 D = $$frac{{400}}{{16}}$$ D = 25 days Total days = 25 + 10 = 35 days

[#225] Computer A takes 3 minutes to process an input while computer B takes 5 minutes. If computers A, B and C can process an average of 14 inputs in one hour, how many minutes does computer C alone take to process one input ?
Correct Answer

(B) 6 minutes

Explanation

Solution: Number of units processed by computer A in 1 minute $$ = frac{1}{3}$$ Number of units processed by computer B in 1 minute $$ = frac{1}{5}{ ext{ }}$$ Number of units processed by computer A, B and C in 1 minute $$eqalign{
& = frac{{14 imes 3}}{{60}} cr
& { ext{ = }}frac{7}{{10}} cr} $$ Number of units processed by computer C in 1 minute $$eqalign{
& = frac{7}{{10}} - left( {frac{1}{3} + frac{1}{5}}
ight) cr
& = frac{7}{{10}} - frac{8}{{15}} cr
& = frac{5}{{30}} cr
& = frac{1}{6} cr} $$ Hence, computer C takes 6 minutes to process one input alone.