Question

A farmer divides his herd of $x$ cows among his $4$ sons so, that first son gets-one-half of the herd, the second son get, one-fourth, the third son gets one-fifth, and the fourth son gets $7$ cows, then the value of $x$ is :

• A. $100$
• B. $140$
• C. $160$
• D. $180$

Answer 1

The correct option is B $140$

Total number of cows $=x$

According to the question, we have
A $=\frac{x}{2}$, $B=\frac{x}{4}$, C $=\frac{x}{5}$, $D=7$
$\therefore$$\frac{x}{2}+\frac{x}{4}+\frac{x}{5}+7=x$
$\Rightarrow$$\frac{10x+5x+4x}{20}=x-7$
$\Rightarrow 19x=20x-140$
$\Rightarrow 140=x$
Hence, option 'B' is correct.