Aptitude 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.**

**Vijaynitj**

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Correction

So if 125 rs we have quantity 100 and for 115 we have quantity new quantity x.then ,

125*X =100*115

**Karan**

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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%

**Radheshyam Shukla**

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

$=\textbf{8%}$

$\text{% Decrease in Petrol Consumption}$

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

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

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

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%