Question

A woman bought 50 dozen eggs at Rs.16 a dozen. Out of these 20 eggs were found to be broken. She sold the remaining egg at Rs.1.50 per egg. Find her gain or loss per cent.

Answer 1

Hint: We can find the cost of 50 dozen eggs using the unitary method, where we know the cost of 1 dozen eggs as Rs.16. We must note that 1 dozen consist of 12 eggs. After finding the number of eggs, we can deduce 20 broken eggs from it. Then again we can find the selling price of the rest of the eggs. Finally, we can find gain / loss by comparing SP and CP.

Complete step-by-step answer:
It is given that a woman bought 50 dozen eggs at Rs.16 a dozen, so from this, we can write that
Cost 1 dozen eggs = Rs.16
Here, we can apply the unitary method. We have the cost of one unit, i.e. a dozen and we have to find cost of 50 units, i.e 50 dozens, so we can multiply the unit cost and number of units as,
\[\therefore \] Cost of 50 dozen eggs = 16 \[\times \] 50 = Rs.800.
Thus the cost price of 50 dozen eggs is Rs.800.
We know that in 1 dozen there are 12 eggs.
\[\therefore \] Total number of eggs = 50 \[\times \] 1 dozen = 50 \[\times \] 12 = 600 eggs.
Now we are told that out of these eggs 20 eggs were found to be broken. Hence we can find the number of eggs remaining as
\[\therefore \] Number of eggs present now = 600 – 20 = 580 eggs.
Now she had to sell these 580 eggs at Rs.1.5 per egg.
\[\therefore \] Selling price = number of eggs \[\times \] cost of each egg = 580 \[\times \] 1.5 = 870 rupees.
Thus we have the selling price (SP) as Rs.870 and the cost price (CP) as 800 rupees.
We can see that the selling price is more than the cost price. Thus she gained and the gain is
Gain = selling price – cost price = 870 – 800 = Rs.70
Hence her gain is Rs.70.
Gain percent can be found from the given formula,
Gain percent = Gain / cost price \[\times \] 100
Gain percent = \[\dfrac{70}{800}\times 100=\dfrac{70}{8}=8.75\]%.
Therefore her gain percent is 8.75%.

Note: Sometimes, students do not think of converting a dozen to single units and they continue with a number of eggs as 50. Then, they deduce 20 from it and continue the calculation further. But, it is mentioned that 20 eggs are broken and not 20 dozen eggs are broken. Hence, this way of solving will lead to wrong answers. Here we got SP > CP, thus it is again. But if CP > SP then it would be a loss for her. Loss percent can be found by the formula,
Loss percent = Loss / cost price \[\times \] 100.