Question

A rod is divided in the ratio 2/5 : 3/10 : 1/2. Total length = 6 m. Find the smallest piece.

• A. 1.5m
• B. 2.5m
• C. 3.5m
• D. 4.5m

Answer 1

Answer:

A. 1.5m

The rod is divided in the ratio:

$\frac{2}{5} : \frac{3}{10} : \frac{1}{2}$

First, convert to whole-number ratios by multiplying each term by the LCM of the denominators (10):

$\frac{2}{5}\times 10 : \frac{3}{10}\times 10 : \frac{1}{2}\times 10$
= 4 : 3 : 5

Total ratio parts:

4 + 3 + 5 = 12

Total length = 6 m, so one part is:

$\frac{6}{12} = 0.5 \text{ m}$

The pieces are:

• $(4 \times 0.5 = 2)$ m

• $(3 \times 0.5 = 1.5)$ m

• $(5 \times 0.5 = 2.5)$ m

Therefore, the smallest piece = 1.5 m.