Question

A certain number of eggs are bought at 4 for 5 and an equal number at 9 for Rs.10. If 15% were broken in transaction and remaining were sold at 2 for Rs.3, find the profit percent and the number of eggs of each kind bought, if Rs.510 were gained on the whole.

Answer 1

Let the number of eggs bought at 4 for Rs.5 be x.
∴ The number of eggs bought at 9 for Rs.10 are x
∴ Total number of eggs bought = x + x = 2x
When eggs are bought at 4 for Rs.5, C.P. of each egg = Rs.${\displaystyle \frac{5}{4}}$
C.P. of x eggs = ${\displaystyle \text{Rs.}\frac{5}{4}x}$
When eggs are bought at 9 for Rs.10, C.P. of each egg =Rs.${\displaystyle \frac{10}{9}}$
C.P. of x eggs  = ${\displaystyle \text{Rs.}\frac{10}{9}x}$
∴  Total C.P.
= ${\displaystyle \text{Rs.}\frac{5}{4}x+\text{Rs.}\frac{10}{9}x}$

= ${\displaystyle \text{Rs.}\frac{85}{36}x}$
Number of eggs broken = 15% of 2x
= ${\displaystyle \frac{15}{100}\times 2x}$

= ${\displaystyle \frac{3x}{10}}$
Eggs left
= ${\displaystyle 2x-\frac{3x}{10}}$

= ${\displaystyle \frac{17x}{10}}$
When eggs are sold at 2 for Rs.3, S.P. of each egg = ${\displaystyle \text{Rs.}\frac{3}{2}}$

S.P. of ${\displaystyle \frac{17}{10}\times \text{eggs}}$

= ${\displaystyle \text{Rs.}\frac{3}{2}\times \frac{17}{10}\times =\text{Rs.}\frac{51}{20}\times }$
Gain = S.P. - C.P.
= ${\displaystyle \frac{51}{20}x-\frac{85}{36}x}$

= ${\displaystyle \left(\frac{459-425}{180}\right)x}$

= ${\displaystyle \frac{34}{180}x}$

= ${\displaystyle \text{Rs.}\frac{17}{90}x}$

Gain % = ${\displaystyle \frac{\text{gain}}{\text{C.P.}}\times 100}$

= ${\displaystyle \frac{\frac{17}{90}x}{\frac{85}{36}x}\times 100}$

= ${\displaystyle \frac{17}{90}\times \frac{36}{85}\times 100}$
= 8%
Also, gain = Rs.510
⇒ ${\displaystyle \frac{17}{90}x}$ = 510

⇒ x = ${\displaystyle \frac{90}{17}\times 510}$
= 2700
∴ Number of eggs of each kind bought = 2700.