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

$\frac{3}{2}$ 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 = $\frac{3}{4}$ 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 = $\frac{3}{5} \times \text{ length of second towel }$

$\frac{3}{4} = \frac{3}{5} \times \text{ length of second towel }\\\\\text{length of second towel }= \frac{5}{4}$

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

$\text{ length of the third towel }= \frac{5}{12} \times (\text{ length of first towel + length of second towel)}$

$\text{ length of the third towel }= \frac{5}{12} \times (\frac{3}{4} + \frac{5}{4}) = \frac{5}{12} \times 2 = \frac{5}{6}$

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 = $\frac{\frac{5}{4}}{\frac{5}{6}}=\frac{5}{4} \times \frac{6}{5}=\frac{3}{2}$

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