Question

I buy 2 machines x and y. x costs rs. 500 more than y. i sell x at a profit of 16% and y at a profit of 7%. my total gain is rs. 1000. the cost of the machine x is:

Answer 1

Profit = 16% of (y+500) + 7% of y = 1000

16% of y + 16% of 500 + 7% of y = 1000

23% of y + 16% of 500 = 1000

23% of y + 80 = 1000

23% of x = 920

            x = 4000           

Answer 2

Machine x costs Rs. 4500.

Given:

Two machines are bought at x and y

x costs Rs. 500 more than y

Profit from x = 16%

Profit from y = 7%

To find:

The cost of machine x

Solution:

Let the price of machine x be a,

Price of Machine y = a-500 [ It is given that x costs 500 more than y]

Profit from machine x = 16% of a = 16/100 * a = 16a/100

Profit from machine y = 7% of (a-500) = 7/100 * (a-500) = 7(a-500) / 100

According to question, total gain = 1000

Total gain = gain on machine x + gain on machine y

1000 = 16a/ 100 + 7(a-500)/100

1000 = 16a/100 + (7a-3500)/100

1000 = (16a + 7a - 3500)/100

1000*100 = 23a - 3500

100000 + 3500 = 23a

103500 = 23a

a = 103500/23

a = 4500

Cost of machine x = a = 4500

Hence the cost of machine x is Rs. 4500.

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