A sells a radio to B at a gain of 10% and B sells it to C at a gain of 5%. If C pays 462 for it, then what did it cost A?

Correct option is A

Given:

- C buys the radio for 462 .
- B sells the radio to C at a gain of 5% .
- A sells the radio to B at a gain of 10% .
Formula Used:

Selling Price and Cost Price Relationship:
If an item is sold at a gain of x% then:
Selling Price (SP)} = $$\text{Cost Price (CP)} \times \left(1 + \frac{x}{100}\right)$$​​
Rearrange to find Cost Price:
Cost Price (CP) = $$\frac{\text{Selling Price (SP)}}{1 + \frac{x}{100}}$$​​
Solution:

Calculate the Cost Price for B (CP of B):
Since C bought the radio for 462 and B sold it to C at a gain of 5% :
CP of B = $$\frac{462}{1 + \frac{5}{100}} = \frac{462}{1.05} = 440$$​​
The Cost Price for A (CP of A):
B bought the radio from A at a gain of 10% :
CP of A =  $$\frac{440}{1 + \frac{10}{100}} = \frac{440}{1.1} = 400$$​​
The cost price for A is 400.