Question

Price of the ticket for movie THE LORD OF RINGS in a cinema is Rs.50. When the price of the ticket was lowered, the number of visitors increased by 60% and the box office collection increased by 36%. Find the reduction in the ticket price.
A man bought 1,000 shares each of face value Rs. 5 at Rs. 7 per share. At the end of the year, the company declared a dividend of 8%. Calculate

(a) the amount of money invested by the man.

(b) the percentage return on his outlay, correct to nearest paise.

Answer 1

Answer on Question #38374 - Math – Algorithms

Suppose the reduction in price equals to $\alpha \in (0,1)$. Then the new price is

$$50 \cdot (1 - \alpha)$$

Since total number of visitors increased by $60\%$, box office collection increased with multiplier

$$(1 - \alpha) \cdot 0.6$$

Thus

$$(1 - \alpha) \cdot 0.6 = 0.36$$ $$1 - \alpha = 0.6$$ $$\alpha = 0.4$$

Thus ticket price reduced by $40\%$.

(a)

The man invested $1000 \cdot Rs.7 = Rs.7000$ money.

(b)

Since dividend equals to 0.08, percentage return on his outlay equals to

$$100\% \cdot \frac{5 \cdot 0.08}{7} = 5.71\%$$