Question

emma can do a piece of work in 57 days olivia is 50% more efficient than emma.the number of days taken by olivia to do same piece of work​

Answer 1

Answer:

38 days

Step-by-step explanation:

O is 50% more efficient than E

Os work =(1+50%)=1.5times of E

O:E=1.5:1=3:2 is ratio in which they work

ratio of no. of days taken O:E = 2:3

E takes 57 days =3parts

1part =19

O takes 2parts =38days

hope this helps

Answer 2

Olivia takes 38 days to do the same piece of work.

Emma can do a piece of work in 57 days. Olivia is 50 % more efficient than Emma.

The number of days taken by Olivia to do the same piece of work.

A/C to question,

Olivia is 50 % more efficient than Emma.

It means, “If the efficiency of Emma is 100 than efficiency of Olivia must be 150.”

∴ The ratio of efficiencies of Emma and Olivia = 100 : 150 = 2 : 3.

We know, efficiency ∝ 1/ number of days.

∴ The ratio of days taken to do the same work by Emma and Olivia = 1/2 : 1/3 = 3 : 2

let proportionality constant is x

no of days taken by Emma = 3x

and number of days taken by Olivia = 2x.

but it has given that Emma can do a piece of work in 57 days.

∴ 3x = 57 ⇒ x = 19

now number of days taken by Olivia = 2x = 2 × 19 = 38 days.

Therefore number of days taken by Olivia is 38 days.