Question

)The cost of A item is increased by 10% and the cost of item B is increased by 18%. Before the price rise, the ratio of the cost of the item A to the cost of the item B was 9 : 2. If the cost of 12 A items and 54 B items before the price rise was Rs C, what is their cost (in Rs) now?

Answer 1

Before price rise:

Let us consider that, the cost of

• A item is Rs. x
• B item is Rs. y

Given:

• x : y = 9 : 2
• or, x/y = 9/2
• or, 2x = 9y ..... (i)

Also given, cost of 12 A items + cost of 54 B items = Rs. C

Then, 12x + 54y = C ..... (ii)

Putting 2x = 9y in (ii), we get

6 (9y) + 54y = C

or, 54y + 54y = C

or, 108y = C

or, y = C/108

So, x = C/24

After price rise:

Cost of A item is increased by 10%.

Then present cost is

= Rs. x * (1 + 10/100)

= Rs. 11x/10

= Rs. 11/10 * C/24

= Rs. 11C/240

Cost of B item is increased by 18%.

Then present cost is

= Rs. y * (1 + 18/100)

= Rs. 59y/50

= Rs. 59/50 * C/108

= Rs. 59C/5400

Answer: Therefore their present cost -

• for A item is Rs. 11C/240 and
• for B item is Rs. 59C/5400.