# Difficult Percentages Solved QuestionAptitude Discussion

 Q. If the price of petrol increases by $25%$ and Raj intends to spend only an additional $15%$ on petrol, by how much $%$ will he reduce the quantity of petrol purchased?
 ✖ A. $10\%$ ✖ B. $12\%$ ✔ C. $8\%$ ✖ D. $6.67\%$

Solution:
Option(C) is correct

Let the price of 1 litre of petrol be Rs. $x$ and let Raj initially buys '$y$' litres of petrol.

Therefore, he would have spent Rs. $xy$ on petrol.

When the price of petrol increases by $25\%$, the new price per litre of petrol is $1.25x$.

Raj intends to increase the amount he spends on petrol by $15\%$.
i.e., he is willing to spend $xy + 15\%$ of $xy = 1.15xy$

Let the new quantity of petrol that he can get be '$q$'.

Then, $1.25x \times q = 1.15xy$

$\Rightarrow q=\dfrac{1.15xy}{1.25x}$

$=\dfrac{1.15y}{1.25}$

$=0.92y$

As the new quantity that he can buy is $0.92y$, he gets $0.08y$ lesser than what he used to get earlier.
Or a reduction of $8\%$.

Edit: For an alternative solution, check comment by Radheshyam Shukla.

Edit 2: For yet another alternative solution, check comment by Chirag Goyal.

Edit 3: For yet another shortcut alternative solution, check comment by Karan.

## (4) Comment(s)

Vijaynitj
()

Lets Assume Initial quantity is 100 and initial price/ltr is 100.

Now price increases by 25 % Means, Price - 125 Rs

Now we will spend only 155 hike means wants to spend only - 115 Rs

and we want to buy same quantity (100 ) in this amount

So if 125 Rs we have quantity x and for 115 we have same 100 quantity than,

125* X = 115* 100

=> x = 92

So Now new quantity is 92

Initial was 100 so Decrement - 8%

Karan
()

if earlier petrol was of Rs 100 , after increase of 25% it becomes 125. But raj intends to spend only Rs 115. Therefore there should be 10/125*100=8%

()

let 1 ltr cost 1 rupees

now again,

1 lt cost is $\frac{125}{115}$

increase$=\frac{125}{115}-1$

% reduction $= \dfrac{\text{inc}*100}{\text{inc}}$

cost $=\dfrac{2*23*100}{23*25}$

$=\textbf{8%}$

Chirag Goyal
()

$\text{% Decrease in Petrol Consumption}$

$=\dfrac{\text{Apparent % Increase in Petrol Price}}{\text{100 + % Increase in petrol price}}\times100$

$=\dfrac{\text{% Increase in Petrol Price - Extra allowed Exemption %}}{\text{100 + % Increase in petrol price}}\times100$

$=\dfrac{\text{25 - 15}}{\text{100 + 25}}\times100$ $=8\%$