Three 262

Three farmers, A, B, and C, hire meadow for Rs 1460. Farmer A puts in 10 cows for 20 days, farmer B 30 cows for 8 days, and farmer C 16 cows for 9 days. Find the rent paid by each one of them.

Correct answer:

A =  500 Rs
B =  600 Rs
C =  360 Rs

Step-by-step explanation:

$$\begin{gathered} a=10\cdot 20=200 \\ b=30\cdot 8=240 \\ c=16\cdot 9=144 \\ s=a+b+c=200+240+144=584 \\ t=1460\text{Rs} \\ A=t\cdot \frac{a}{s}=1460\cdot \frac{200}{584}=\frac{1460\cdot 200}{584}=\frac{292000}{584}=500\text{Rs} \end{gathered}$$

$B=t\cdot \frac{b}{s}=1460\cdot \frac{240}{584}=\frac{1460\cdot 240}{584}=\frac{350400}{584}=600\text{Rs}$

$C=t\cdot \frac{c}{s}=1460\cdot \frac{144}{584}=\frac{1460\cdot 144}{584}=\frac{210240}{584}=360\text{Rs}$

Try another example