Question

With Rs. $1000$ a rancher is to buy steers at Rs. $25$ each and cows at Rs. $26$ each. If the number of steers $s$ and the number of cows $c$ are both positive integers, then:

• A. this problem has no solution
• B. there are two solutions with $s$ exceeding $c$
• C. there are two solutions with $c$ exceeding $s$
• D. there is one solution with $s$ exceeding $c$
• E. there is one solution with $c$ exceeding $s$

Answer 1

Answer: (E)

there is one solution with $c$ exceeding $s$

$25s+26c=1000$; $\therefore$ $s=\frac{40-26c}{25}$
The only solution in positive integers is $c=25;s=14$