Question

After selling 10 candles a man earns a profit of the selling price of 3 bulbs. While selling 10 bulbs a man loses selling price of 4 candles. The numerical value of p% and l% is equal and the cost price of the candle is half of the cost price of the bulbs. Find the ratio of selling price of the candles to bulbs.
(a) 5 : 4
(b) 3 : 2
(c) 4 : 5
(d) 3 : 4

Answer 1

Hint:We start solving the problem by assigning variables x and y to the cost prices and selling prices of candle and bulb respectively. We then use the condition that the cost of a candle is half the cost of the bulb to get the relation between the cost prices. We then find the profit percentage and loss percentage using the standard definition and equal them. We then use the relation of cost of candle and bulb in this equation and make the necessary calculations to get the required value.

Complete step by step answer:
We have been said that a man selling 10 candles can earn a profit of selling price of 3 bulbs and by selling 10 bulbs he gets a loss of SELLING PRICE of 4 candles. The numerical values of profit percentage and loss percentage are equal and the cost of the candle is half the cost of the bulb. We need to find the ratio of selling price of the candles to the bulbs.
Let us consider the cost price of candles as x and the cost price of bulbs as y. Similarly, let us consider the selling price of candles as ‘a’ and that of bulbs as ‘b’.
We have a cost of the candle is half the cost of the bulb.
So, we have $x=\dfrac{y}{2}$ ---(1).
We have our first condition that after selling 10 candles the man earns a profit of SELLING PRICE of 3 bulbs.
Profit percentage = (Profit for selling 10 candles / COST PRICE of 10 candles) \[\times \] 100.
Profit percentage = (selling price 3 bulbs / COST PRICE of 10 candles) \[\times \] 100.
Profit percentage = $\dfrac{3b}{10x}\times 100$ ---(2).
We have our second condition that by selling 10 bulbs gets a loss of selling price of 4 candles.
Loss percentage = (loss of selling of 10 bulbs / COST PRICE of 10 bulbs) \[\times \] 100.
Loss percentage = (selling price of 4 candles / COST PRICE of 10 bulbs) \[\times \] 100.
Loss percentage = $\dfrac{4a}{10y}\times 100$ ---(3).
Now it has been told that the numerical value of profit % and loss % are equal.
\[\therefore \] Profit percentage = Loss percentage.
From equations (2) and (3).
\[\Rightarrow \dfrac{3b}{10x}\times 100=\dfrac{4a}{10y}\times 100\].
From equation (1), we get
\[\Rightarrow \dfrac{3b}{10\left( \dfrac{y}{2} \right)}\times 100=\dfrac{4a}{10y}\times 100\].
\[\Rightarrow \dfrac{6b}{10y}\times 100=\dfrac{4a}{10y}\times 100\].
Let us cancel out the like terms and get a ratio of a and b.
\[\Rightarrow 6b=4a\].
\[\Rightarrow \dfrac{a}{b}=\dfrac{6}{4}\].
\[\Rightarrow \dfrac{a}{b}=\dfrac{3}{2}\].
So, we have found the ratio of the selling price of the candle and bulb as $3:2$.
∴ The correct option for the given problem is (b).

Note:
We know that the formula for profit and loss percentage is actually profit or loss of the product by the cost price. So, be careful while you make the expression for profit and loss from the given information. We are supposed to find the ratio of selling price of candles to bulbs, and we have been given that after selling 10 candles a man earns a profit of the selling price of 3 bulbs and after selling 10 bulbs a man loses the selling price of 4 candles. We might directly try to write the ratio as 3:4 without doing proper calculations, selling price especially while appearing for competitive exams. This is wrong because in the question, we have the cost price of the candle is half of the cost price of the bulbs. So, this information must be taken into consideration