Question

A farmer divides his herd of $n$ cows among his four sons so that one son gets one-half the herd, the second, one-fourth, the third son, one-fifth and the fourth, $7$ cows, then $n$ is

• A. $180$
• B. $140$
• C. $240$
• D. $100$

Answer 1

The correct option is B $140$

There are $n$ cows:
First son gets: $\frac{n}{2}$

Second son gets: $\frac{n}{4}$

Third son gets: $\frac{n}{5}$

Fourth son gets: $7$ cows
Therefore, sum of cows each son gets equals the total number of cows
$\frac{n}{2}+\frac{n}{4}+\frac{n}{5}+7=n$
$7=\frac{n}{20}$
$n=140$