Question

The price of a pencil box is Rs. 70. If the price of the pencil box is reduced such that the ratio of the original price to the new price is 14:13, what will be the reduced price of the pencil box?
(a)60
(b)65
(c)75
(d)80

Answer 1

Hint: The given is the ratio of the old price $:$ new price. So, use the basic definition of ratio, equate it with the ratio of old and new price and solve.

Complete step-by-step answer:
Let us first know what a ratio is.
A ratio, in basic words, is a quantity used to define a comparison between two quantities. A bit toward the advanced side, it is the quantity which defines how many times of one quantity is that of others.
At our level, apart from the definition, we will treat it as a simple fraction that defines a relation between two given quantities.
Now, starting with the question.
Given;
The original price of a pencil box before the reduction of price was Rs. 70.
And generally, in such questions, we let the unknown part be x.
So, here we let the new price be x.
Now, according to the definition of ratio, a ratio a : b= $\dfrac{a}{b}$ .
$\therefore 14:13=\dfrac{14}{13}$
Applying this to find the new price of the pencil box:
$\dfrac{14}{13}=\dfrac{\text{original price}}{\text{new price}}$
$\Rightarrow \dfrac{14}{13}=\dfrac{70}{x}$
On cross-multiplication, we get:
$14x=70\times 13$
$\Rightarrow 14x=910$
$\Rightarrow x=\dfrac{910}{14}$
$\therefore x=65$
Hence, the correct option is (b) 65 i.e., the reduced price of the pencil box is Rs. 65.

Note: Read the question carefully as in the question including ratio, there is always a chance that the question might have a twist hidden in the words of the question. For instance, in the question it is given ‘reduced’ but the ratio is indicating an increase, then it is always preferred to go with the ratio, as at the end, the ratio will be giving us the answer. Also, have a look at the options too.