Question

A television manufacturing company declares that a television is now available for Rs. 5600 as against Rs. 8400 one year before. Find the percentage reduction in the price of television offered by the company.
(a) $ \dfrac{100}{9}\% $
(b) $ \dfrac{5}{9}\% $
(c) $ \dfrac{21}{25}\% $
(d) $ \dfrac{100}{3}\% $

Answer 1

Hint: First of all, we will find the reduction in price of the Television set in the last year. Then we will find how much percentage does the reduction accounts for out of the initial price by the relation pc = $ \dfrac{c}{i}\times 100\% $ , where pc is the percentage change, c is the change in the price and i is the initial price. This will give us the percentage reduction in the price of the television offered by the company.

Complete step-by-step answer:
It is given that in the previous year, the price of the television was Rs 8400 and the price has reduced to Rs 5600.
Thus, the change in the price = c = 8400 – 5600 = 2800.
This means, over a year, the price of the television reduced by Rs 2800.
Now, we will find how much percentage this change, i.e. Rs 2800 accounts of the initial price of the television, i.e. Rs 8400.
We can find it by the relation pc = $ \dfrac{c}{i}\times 100\% $ , where pc is the percentage change, c is the change in the price and i is the initial price.
Thus, c = 2800 and i = 8400
 $ \Rightarrow $ pi = $ \dfrac{2800}{8400}\times 100\% $
 $ \Rightarrow $ pi = 0.333 $ \times $ 100 %
 $ \Rightarrow $ pi = 33.33 %
Therefore, the price of the Television set decreased by 33.33 %. Now, 33.33 can also be expressed as $ \dfrac{100}{3} $ .
Thus, the price of the Television set decreased by $ \dfrac{100}{3}\% $ .
Hence, option (d) is the correct option.

Note: Students can directly find the percentage decrease by the relation $ \text{pd = }\dfrac{{{v}_{1}}-{{v}_{2}}}{{{v}_{1}}}\times 100\% $ . If we apply this, we can skip the extra step of finding the difference separately.