Question

A man buys 3 type 1 cakes and 6 type 2 cakes for 900. He sells type 1 cakes at a profit of 15% and type 2 cakes at a loss of 10%. If his overall profits is 30, the cost price of a type 1 and of a type 2 is

Answer 1

3a + 6b = 900 i.e. a + 2b = 300 ;
3a x 15/100 (profit by cake of type 1) - 6b x 10/100(loss by cake of type 2) = 30 ;
two equation and two variable
a = 160 and b = 70
a is cake of type 1 and b is cake of type 2

Answer 2

The price of type 1 cake is 160 and price of type 2 cake is 70.

Solution:

Given:

Type 1 = 3 Cakes

Type 2 = 6 Cakes

Total = Rs. 900

Type 1 Cake Profit = 15 %

Type 2 Cake Loss = 10 %

Overall Profit = Rs. 30

3a + 6b = 900  

i.e., a + 2b = 300 ______(1)

$\begin{array}{l}{3 a \times \frac{115}{100}+6 b \times \frac{90}{100}=930} \\\\ {\frac{3}{100}(115 a+180 b)=930} \end{array}$

115 a+180 b=31000 ______(2)

Solving (1) and (2) we get a = 160, b= 70.