Question

A trader purchased a wall clock and a watch for a sum of 5070. He sold them making a profit of 10% on the wall clock and 15% on the watch. He earns a profit of Rs
669.50. Find the cost price of the wall clock and that of the watch.

Answer 1

Step-by-step explanation:

A trader purchases a wall clock and a watch. The total cost of these two items is Rs.5070

Let us take the price of one wall clock as Rs.x, then the price of one watch will be Rs. (5070-x)

After buying the items, the trader sells them earning profit. It means he is selling the items at a cost higher than the cost he bought them.

Profit % earned on the wall clock is 10.

We know how to calculate the profit%. We will use the below formula to calculate,

Profit % = (Selling Price-Cost PriceCost Price)×100

Profit % = (Selling Price-Cost PriceCost Price)×100

Cost price of wall clock is 'x'

Profit % is 10

Putting these values in the formula stated above, we get

10=(SP−xx)×100 . . . . . . . . . . . . . (1)

10=(SP−xx)×100 . . . . . . . . . . . . . (1)

Now, profit earned on watch is 15%

Cost price of 1 watch is Rs.(5070-x)

Suppose that, selling price of 1 watch is SP′SP′, then, putting these values in formula stated earlier, we get

15=SP′−(5070−x)(5070−x)×100 . . . . . . . . . . . . . (2)

15=SP′−(5070−x)(5070−x)×100 . . . . . . . . . . . . . (2)

We are given with one more important information, that, the total profit not the profit % in Rs is Rs.699.50

Since, Profit = Selling price - Cost price ⇒ SP-CP

Profit = Selling price - Cost price ⇒ SP-CP

From equation (1) and (2) we get,

SP−CP=10100×(x)SP′−CP′=15100×(5070−x)

SP−CP=10100×(x)SP′−CP′=15100×(5070−x)

Addition of these two equation would lead to the total profit earned in Rs, we get

10x100+15(5070−x)100=Rs.699.50⇒0.1x+760.5−0.15x=699.50⇒−0.05x+760.5=699.50⇒0.05x=61⇒x=1220

10x100+15(5070−x)100=Rs.699.50⇒0.1x+760.5−0.15x=699.50⇒−0.05x+760.5=699.50⇒0.05x=61⇒x=1220

The cost price of the wall clock was x i.e. x = Rs.1220

The cost price of the watch was (5070-x) i.e. Rs.3850

Note: This question can also be directly solved by adding the 10% of the cost price of the wall clock, which is assumed as x and 15% of the cost price of watch, which is (5070-x) and then taking the sum of these to be Rs.699.50.

Therefore, we will get the equation as, 10x100+15(5070−x)100=699.50

10x100+15(5070−x)100=699.50