Question

2 gents and 5 ladies complete a work in 4 days to complete the same work. Then how many days need to complete the same work for single gent or lady

Answer 1

Answer:

A single gent can complete the work in 18 hours and a single lady can complete the work in 36 hours.

Step-by-step explanation:

Let the work done by 1 gent alone be m and work done by 1 lady alone be n

Combined rate of work done = 1/4

2m + 5n = 1/4

8m + 20n = 1

n = (1-8m)/20.....(1)

work done by gent + work done by lady = 12

m + n = 1/12

12m + 12n = 1

12m + 12[(1-8m)/20] = 1 ....(from equation 1)

12m + (12-96m)/20 = 1

(240m + 12 - 96m) / 20 = 1

144m + 12 = 20

144m = 20-12

144m = 8

m = 8/144

m = 1/18.....putting in (3)

n = [1-8(1/18)]/20

n = (1 - 4/9)/20

n = (9-4/9)/20

n = (5/9)/20

n = 5/9 × 1/20

n = 5/180

n = 1/36

Hence, work done by 1 gent and 1 lady is 1/18 and 1/36respectively.

so, time taken taken by 1 gent is 18 hours and time taken by 1 lady is 36 hours.

#BAL

#ANSWERWITHQUALITY