A man sold his radio-set at a loss of 20%.If he would have sold it for ₹90 more, his loss would have been only 10%. Find cost price of radio-set.
If the cost was c and the selling price was p,
p = 0.80c
p+90 = 0.90c
Now just solve for c.
Or, consider that the extra 90 is 10% of the cost. So, the cost was 900.
Let's assume the cost price of the radio-set is 'C'.
According to the given information, the man sold the radio-set at a loss of 20%. This means he sold it for 80% of the cost price, which can be expressed as:
Selling price = C * 80/100 = 0.8C
If he had sold it for ₹90 more, his loss would have been only 10%. This means he would have sold it for 90% of the cost price, which can be expressed as:
Selling price = C * 90/100 = 0.9C
From the above equations, we can set up the following equation:
0.8C + 90 = 0.9C
Subtracting 0.8C from both sides gives:
90 = 0.1C
Dividing both sides by 0.1 gives:
C = 900
Therefore, the cost price of the radio-set is ₹900.
To find the cost price of the radio-set, we can set up a system of equations. Let's call the cost price of the radio-set "x."
According to the given information, the man sold the radio-set at a loss of 20%. This means he sold it for 80% of its cost price.
So, the selling price of the radio-set is 80% of the cost price, which can be expressed as 0.8x.
If the man had sold it for ₹90 more, his loss would have been only 10%. This means he would have sold it for 90% of its cost price.
So, the selling price of the radio-set (if he had sold it for ₹90 more) is 90% of the cost price, which can be expressed as 0.9x.
Now, we have two equations:
1) Selling price at a loss of 20%: 0.8x
2) Selling price at a loss of 10% (if ₹90 more): 0.9x
We can write these equations as follows:
0.8x = 0.9x - ₹90
To solve this equation, we can isolate the x term:
0.8x - 0.9x = -₹90
-0.1x = -₹90
x = -₹90 / -0.1
x = ₹900
Therefore, the cost price of the radio-set is ₹900.