Percentages Quiz Set 003

Let the numbers be x and x - 120. We have been given x = $65/100$ × (x + x - 120), which gives 100x = 65 × (2x - 120), solving, we get x = 260.

Let us derive the shortcut formula first, so that you can remember it and use it when the need arises. Suppose the number is 100, and let the increase be x%. The number becomes 100 + x. When it is reduced by x%, we get 100 + x - $((100 + x) × x)/100$ = 100 + x - $(x + x^2/100)$ = 100 - $x^2/100$, hence a reduction of $x^2/100$ = 16%

Let the items be x. His % stock left is 100 - 75 = 25, so 25% of x = 200, which gives x = $200/25$ × 100 = 800 items.

Let the calls be for Rs. x. The total bill is x + 5% of x = ${21x}/20 = 525$, which gives x = Rs. 500.

Let the numbers be x and ${114x}/100$. The sum is x + ${114x}/100$ which is same as ${214x}/100 = 1712$. Solving we get the smaller number x = 800.