CAT 2022 Slot 3 QA Question 17: A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possib

Question

A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possib

Accepted Answer

Let the numbers of ₹100, ₹250 and ₹500 cheques be $a$, $b$ and $c$ respectively.
$a + b + c = 100$
$100a + 250b + 500c = 15250$
Divide the amount equation by 50.
$2a + 5b + 10c = 305$
Also multiply the cheque-count equation by 2.
$2a + 2b + 2c = 200$
Subtracting gives
$3b + 8c = 105$
We need the max

A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is