ISI Maths

Question

A, B and C are three commodities. A packet containing 5 pieces of A, 3 of B and 7 of C costs Rs. 24.50.

A packet containing 2, 1 and 3 of A, B and C respectively, costs Rs. 17.00. The cost of a packet containing 16, 9 and 23 items of A, B and C respectively

(A) is Rs. 55.00;                 (B) is Rs. 75.50;

(C) is Rs. 100.00;     (D) cannot be determined from the given information.

Answer 1

Ans C

Let unit price for A, B and C are a,b, and c

So given data can be written as equation as 

5a+3b+7c =24.5          $\dots (1)$

2a+b+3c=17                $\dots (2)$

We need to calculate 16a+9b+23 c

Multiply (1) with 3 we get  

15a+9b+21c=73.5                   $\dots (4)$

Multiply equation(2) with 3 and subtract (1)

3(2a+b+3c)-(5a+3b+7c)=17*3-24.5

a+2c=26.5                             $\dots (5)$

add (4)+(5)

( 15a+9b+21c)+(a+2c)= 73.5+26.5 

16a+9b+23 c=100