# CAT 2022 Set-3 | Quantitative Aptitude | Question: 1

1,703 views
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

Let no. of ₹100, ₹250 and ₹500 cheques are x, y and z respectively. And the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250.

So, x+y+z = 100  &  100x+250y+500z = 15250  => 2x+5y+10z = 305

By eliminating x from 2nd equation we get, 2(100-y-z)+5y+10z=305  => 3y+8z = 105

The range of values of x, y and z are all non negative integers from 0 to 100. If we see equation

3y+8z = 105, we will notice that for max value of z, the value of y should be minimum. So, we will hit and try the possible value of y starting from 0, for max value of z.

z = (105 – 3y) / 8

Here y = 0, 1, 2 will not result an integer value of z, but y = 3 will. So, when y = 3, then z = 12.

## Related questions

If $c=\dfrac{16 x}{y}+\dfrac{49 y}{x}$ for some non-zero real numbers $x$ and $y,$ then $c$ cannot take the value$-60$ $-50$ $60$ $-70$
If $(3+2 \sqrt{2})$ is a root of the equation $a x^{2}+b x+c-0$, and $(4+2 \sqrt{3})$ is a root of the equation $a y^{2}+m y+n – 0$, where $a, b, c, m$ and $n$ are inte...
Suppose the medians $\mathrm{BD}$ and $\mathrm{CE}$ of a triangle $\mathrm{ABC}$ intersect at a point $\mathrm{O}$. If area of triangle $\mathrm{ABC}$ is $108$ $\mathrm{s... 1 votes 0 answers 4 404 views Bob can finish a job in$40$days, if he works alone. Alex is twice as fast as Bob and thrice as fast as Cole in the same job. Suppose Alex and Bob work together on the f... 1 votes 0 answers 5 433 views A glass contains$500 \mathrm{cc}$of milk and a cup contains$500 \mathrm{cc}$of water. From the glass,$150 \mathrm{cc}\$ of milk is transferred to the cup and mixed th...