Percentages Quiz Set 015

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 100 = Rs. 200/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 200 × c, which gives c = 100/200, so the decrease is 1 - $100/200$ = ${200 - 100}/200$ × 100% = 50%.

We can drop the % from both sides and write the given equation as 13X + 2Y = $2/3$ × (11X + 15Y), which is same as 3 × (13X + 2Y) = 2 × (11X + 15Y). Let r = X/Y. Dividing both sides by Y and putting r = X/Y, we get, 3 × (13r + 2) = 2 × (11r + 15), solving for r we get r = ${24/17}$, which is same as: $1{7/17}$.

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 $x^2/100$ = 64%

Let price be Rs. 100/kg and the consumption be 1 kg. The current expenditure is 100 × 1 = Rs. 100. The new price of sugar is 100 + 40 = Rs. 140/kg. Let the new consumption be c kg. Now, if expenditure is to be same we should have 100 = 140 × c, which gives c = 100/140, so the decrease is 1 - $100/140$ = ${140 - 100}/140$ × 100% = ${200/7}$, which is same as: $28{4/7}$%.

The %age ≥ 50°C = (100 - 30) = 70. If x is the size of the sample, 70% of x = 1260 + $2/3 × 1260$ = ${5 × 1260}/3$, which is same as ${70 × x}/100$ = ${5 × 1260}/3$. Solving, we get x = 3000.