Question

Entry fee in an exhibition was Rs.1. Later this was reduced by 25% which increased the sale by 20%. Then find the percentage of slump in business.

Answer 1

Hint: First of all, consider the total original sale in the exhibition as Rs.100 and calculate the decreased entry fee and the increased sale of the exhibition. Then find the increase in the number of visitors which is the difference of the present number of visitors and the past number of visitors.

Complete step-by-step answer:

Let the total original sale in the exhibition be Rs.100.

As the entry fee in the exhibition is Rs.1, the number of visitors = 100

Later the entry fee was reduced by 25%.

Now the entry fee will be \[1 - 1 \times \dfrac{{25}}{{100}} = 1 - 0.25 = Rs.0.75\]

Given that the sale is increased by 20%.

So, the present sale is \[100 + 100 \times \dfrac{{20}}{{100}} = 100 + 20 = Rs.120\]

Now consider the present number of visitors.

The present number of visitors \[ = \dfrac{{{\text{Present sale}}}}{{{\text{Reduced entry fee}}}}\]

                                                        \[ = \dfrac{{120}}{{0.75}} = 160\]

Increase in the number of visitors = present number of visitors – past number of visitors

                                                             = 160 – 100 = 60

Thus, the percentage increase in visitors \[ = \dfrac{{{\text{Increase in the number of

visitors}}}}{{{\text{past number of visitors}}}} \times 100\]

                                                                         \[ = \dfrac{{60}}{{100}} \times 100 = 60\% \]

Hence, the percentage of the increase in the business is 60%.

Note: Here we have taken the original sale in the exhibition as Rs.100 because this will lead us to have simple calculations in the entire solution as this problem is related to increase and decrease in percentage.