Question

$\text{A metal rod of length}4\frac{3}{8}\text{m is subjected to the following changes.}$


$\text{The final length of the rod will be}$

• A. $6\frac{7}{8}m$
• B. $7\frac{7}{8}m$
• C. $6\frac{5}{8}m$
• D. $7\frac{5}{8}m$

Answer 1

The correct option is B $7\frac{7}{8}m$

Calculating the length of the rod at each step, we get:

$\text{Step 1: The rod of length}4\frac{3}{8}\text{m is}shortened\text{by}2\frac{1}{8}\text{m}$

$\therefore \text{Length after step 1}$

$=4\frac{3}{8}\text{m}-2\frac{1}{8}\text{m}$

$=(4-2)\text{m}+(\frac{3}{8}-\frac{1}{8})\text{m}$

$=2\text{m}+\frac{(3-1)}{8}\text{m}$

$=2\text{m}+\frac{2}{8}\text{m}$

$=2\frac{2}{8}\text{m}$

$\text{Step 2: The rod length is}lengthened\text{by}5\frac{5}{8}\text{m}$

$\therefore \text{Length after step 2}$

$=2\frac{2}{8}\text{m}+5\frac{5}{8}\text{m}$

$=(2+5)\text{m}+(\frac{2}{8}+\frac{5}{8})\text{m}$

$=7\text{m}+\frac{(2+5)}{8}\text{m}$

$=7\text{m}+\frac{7}{8}\text{m}$

$=7\frac{7}{8}\text{m}$

$\therefore \text{The final length of the metal rod will}\text{be}7\frac{7}{8}\text{m.}$