Question

You have towels of 3 sizes. The length of one of them is equal to 3/4m, which makes up 3/5 of the length of the second. The length of the third towel makes up 5/12 of the lengths of the first 2. What part of the length of the third towel is the length of the second towel?

Answer 1

`(3)/(2)` part of length of the third towel is the length of the second towel

Solution:

Given that You have towels of 3 sizes

Length of the first towel =
`(3)/(4)` meter

The length of one of them is equal to 3/4m, which makes up 3/5 of the length of the second.

Length of the first towel =
`(3)/(5) * \text{ length of second towel }`

`(3)/(4) = (3)/(5) * \text{ length of second towel }\\\\\text{length of second towel }= (5)/(4)`

The length of the third towel makes up 5/12 of the lengths of the first 2.

`\text{ length of the third towel }= (5)/(12) * (\text{ length of first towel + length of second towel)}`

`\text{ length of the third towel }= (5)/(12) * ((3)/(4) + (5)/(4)) = (5)/(12) * 2 = (5)/(6)`

To find: What part of the length of the third towel is the length of the second towel ?

Ratio of second to third towel length =
`((5)/(4))/((5)/(6))=(5)/(4) * (6)/(5)=(3)/(2)`

Thus 3/2 part of length of the third towel is the length of the second towel