Question

Solving $(12.5\times 30)+(\frac{1}{5}\times 15)-(8\times 30)+(\frac{2}{5}\times 15)$, we get

• A. 122
• B. 135
• C. 144
• D. 156

Answer 1

The correct option is C

144

$(12.5\times 30)+(\frac{1}{5}\times 15)-(8\times 30)+(\frac{2}{5}\times 15)$

We shall rearrange the above as follows:

$\left[\right(12.5\times 30)-(8\times 30\left)\right]+\left[\right(\frac{1}{5}\times 15)+(\frac{2}{5}\times 15\left]\right)$

We know, multiplying two numbers by a number separately and adding give the same result as multiplying their sum by the number.

i.e. $xz+yz=(x+y)z$, for all numbers $x,y,z$

Also we know, multiplying two numbers by a number separately and subtracting give the same result as multiplying their difference by the number.

i.e. $xz-yz=(x-y)z$, for all numbers $x,y,z$

So,

$\left[\right(12.5\times 30)-(8\times 30\left)\right]+\left[\right(\frac{1}{5}\times 15)+(\frac{2}{5}\times 15\left]\right)$

= $\left[\right(12.5-8)\times 30]+\left[\right(\frac{1}{5}+\frac{2}{5})\times 15]$

= $[4.5\times 30]+[\frac{3}{5}\times 15]$

= $135+9$

= $144$