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 possible number of cheques of ₹500 that the donation box may have contained,is

Answer 1

Correct Answer: 12

We are given that the donation box contains exactly 100 cheques amounting to a total sum of ₹15250. Let the number of ₹100, ₹250, and ₹500 cheques be represented by x, y, and z respectively.

1. We can set up two equations based on the given information:
- x + y + z = 100 (since there are 100 cheques)
- 100x + 250y + 500z = 15250 (total sum of money)

2. From the first equation, we can express x in terms of y and z:
x = 100 - y - z

3. Substituting the value of x from the first equation into the second equation:
100(100 - y - z) + 250y + 500z = 15250
10000 - 100y - 100z + 250y + 500z = 15250
150y + 400z = 5250
3y + 8z = 105

4. We want to maximize the number of ₹500 cheques (z). Since we are working with positive integer values, we can try different values of y and calculate the corresponding value of z to see if it results in a positive integer.

- For y = 0, z = 105/8 = 13.125 (not a positive integer)
- For y = 1, z = 102/8 = 12.75 (not a positive integer)
- For y = 2, z = 99/8 = 12.375 (not a positive integer)
- For y = 3, z = 96/8 = 12 (a positive integer)

5. So, when y = 3, the value of z becomes 12, which is a valid integer value.

Hence, the maximum possible number of ₹500 cheques in the donation box is 12 (Ans: 12).