Question

A reduction of 20% in the price of rice enables a person to buy 3.5kg more for Rs77. Then the original price per kg is:
$
  {\text{A}}{\text{. Rs 4}}{\text{.00}} \\
  {\text{B}}{\text{. Rs 4}}{\text{.50}} \\
  {\text{C}}{\text{. Rs 5}}{\text{.00}} \\
  {\text{D}}{\text{. Rs 5}}{\text{.50}} \\
$

Answer 1

Hint: Consider actual price of the rice bag be Rs. a per kg, then new price will be difference of actual price and 20% reduction of actual price and consider it as Rs p per kg.Calculate quantity of rice bought by dividing price with buying price.Now difference of quantity of rice bought i.e quantity of rice bought at original price and actual price is equal to quantity of rice bought extra 3.5kg at reduced price. Equating this equation we will get the value of original price per kg.

Complete step-by-step answer:
Let the actual price of the rice bag be Rs. a per kg
Let the new price of the rice bag be Rs. p per kg

Given Data: New price = 20% reduction in actual price
                                  $
   \Rightarrow {\text{p = a - a}} \times \dfrac{{20}}{{100}} \\
   \Rightarrow {\text{p = }}\dfrac{{{\text{4a}}}}{5}{\text{ per kg}}{\text{.}} \\
$

Given Data: A reduction of 20% in the price of rice enables a person to buy 3.5kg more for Rs77.
(This means we can buy 3.5 kgs extra when the rice is bought at a reduced price than what we buy at the original price.)
The quantity of rice bought =$\dfrac{{{\text{price}}}}{{{\text{buying price}}}}$.
Now the difference in quantity of rice bought = Quantity of rice bought at original price – Quantity of rice bought at reduced price.

i.e. $\dfrac{{77}}{{\left( {\dfrac{{{\text{4a}}}}{5}} \right)}} - \dfrac{{77}}{{\text{a}}} = 3.5$
⟹$\dfrac{{385}}{{{\text{4a}}}} - \dfrac{{77}}{{\text{a}}} = 3.5$
⟹$385 - \dfrac{{308}}{{4{\text{a}}}} = 3.5$
⟹$\dfrac{{77}}{{4{\text{a}}}} = {\text{ 3}}{\text{.5}}$
$ \Rightarrow \dfrac{{77}}{{14}} = {\text{a}}$
⟹a = 5.5

The original price of the rice per kg is Rs 5.5/kg

Note: In order to solve questions of this type the key is to write the given sentences in the question into equations using the variables, we reduce one variable into another and solve for the other variable accordingly to find the answer.