Question

A farmer divides his herd of k cows among his 4 sons, so that one son gets one half of the herd, the second gets one-fourth, the third gets one-fifth and the fourth gets 9 cows. Then k is equal to ?

Answer 1

Answer:

k=180

Step-by-step explanation:

It is given that:

• The first son gets $\frac{1}{2}k$
• The second son gets $\frac{1}{4}k$
• The third son gets $\frac{1}{5}k$
• The fourth son gets $9$ cows

We now need to calculate how much those 9 cows the fourth son gets, represent as a ratio:

$r=1-(\frac{1}{2}+\frac{1}{4}+\frac{1}{5})=\frac{1}{20}$

Therefore,

$\frac{1}{20}k=9\\ k=180$

Answer 2

Answer:

Step-by-step explanation:

$According\:to\:the\:given\:data,\\First\:son's\:share=\frac{k}{2}\\Second\:son's\:share=\frac{k}{4}\\Third\:son's\:share=\frac{k}{5}$

$Fourth\:son's\:share=9\:cows$

$=>\frac{k}{2}+\frac{k}{4}+\frac{k}{5}+9=k\\\\=>\frac{10k+5k+4k+180}{20}=k$

10k+5k+4k+180=20k

180=20k-19k

k=180