Time And Work - Study Mode
[#191] Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take $$frac{8}{3}$$ more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs. 450, then in how many days did A, B and C together complete the whole work?
Correct Answer
(B) 4 days
Explanation
Solution: Ratio of efficiencies of A, B and C, = 5x : 4x : 6x Number of days required by A and B = $$frac{{100}}{{9{ ext{x}}}}$$ ------ (1) Number of days required by A, B and C = $$frac{{100}}{{15{ ext{x}}}}$$ ------ (2) $$eqalign{
& frac{{100}}{{9{ ext{x}}}} - frac{{100}}{{15{ ext{x}}}} = frac{8}{3} cr
& Rightarrow { ext{x}} = frac{5}{3} cr} $$ Number of days required by A, B and C = $$frac{{100}}{{15{ ext{x}}}}$$ = $$frac{{100}}{{15 imes frac{5}{3}}}$$ = 4 days
[#192] Two men and women are entrusted with a task. The second man needs three hours more to cope up with the job than the second man and the woman would need working together. The first man, working alone, would need as much time as second man and the woman working together. The first man working alone, would spend eight hours less than the double period of the time second man would spend working alone. How much time would the two men and the women need to complete the task if they all asked together?
Correct Answer
(A) 1 hour
Explanation
Solution: Difference in times required by the first man (A) and second man (B) = 3 hours. Also, if t a and t b are the respective times, then
t b - t a = 3 . . . . . . . . . ..(1)
Also, B alone be take = (t a + 3) h
According to the question, 2t b - t a = 8 2 × (t a + 3) - t a = 8 [Using equation (1)] t a = 2 hours. Now B and woman together take 2 hours and A also take 2 hours, so time required will be half when all 3 work together. So in 1 hour work would be completed.
[#193] At a Tech Pvt Ltd. there are some engineering students employed as trainee engineers, belong to two eminent institutions of India. One group belongs to IIT and another to NIT. Each student of IIT works for 10 hours a day till 60 days and each student of NIT works for 8 hours a day till 80 days on the two same project. The ratio of students of IIT and that of NIT is 4:5 respectively. Students of which institution is slower in work and by how much?
Correct Answer
(C) NIT is 25% less efficient
Explanation
Solution: Let E 1 and E 2 are the working efficiency of each student of IIT and NIT per hour respectively. Using work equivalence method, 4 × 10 × 60 × E 1 = 5 × 8 × 80 × E 2 $$frac{{{{ ext{E}}_1}}}{{{{ ext{E}}_2}}} = frac{4}{3}$$ As, 3E 1 = 4E % less efficient of NITians = $$frac{{1 imes 100}}{4}$$xa0 = 25% Thus, each engineer from NIT is 25% less efficient than that of IIT.
[#194] 42 women can do a piece of work in 18 days, How many women would be required do the same work in 21 days.
Correct Answer
(B) 36
Explanation
Solution: Let X be the number of women required to finish the work in 21 days. Now, using Work Equivalence Method: 42 × 18 = X × 21 X = 36. Number of women required = 36
[#195] Vijay can chop all the vegetables available in 4 minutes lesser time than Bishaka. If both of them work together, they take 288 seconds to chop all the vegetables. How long does Vijay alone take to chop all the vegetables?
Correct Answer
(C) 8 min
Explanation
Solution: By the option ⇒ $$frac{{24}}{5}$$ = 4.8 minutes = 288 seconds (satisfied)