I bought a certain number of apples at 4 for 6 paise and 3/5 of that number at 3 for 6 paise by selling them at 16 for rs.30p. I gained 24 paise.. How many apples did I buy????
To find out how many apples you bought, we need to break down the problem step by step and solve it using algebra.
Let's assume that the number of apples you bought initially is 'x'.
According to the given information:
- You bought x apples at 4 for 6 paise, which means for every 4 apples, you paid 6 paise.
- Then, you bought 3/5 (or 3x/5) of the initial number of apples at 3 for 6 paise. So, for every 3 apples, you paid 6 paise.
- Finally, you sold the apples at 16 for Rs. 30p, which means for every 16 apples, you received Rs. 30p.
Now, let's solve the equation step by step to find the value of x:
1. The cost of buying the initial x apples = (x/4) * 6 = 6x/4 = 3x/2 paise
2. The cost of buying the additional (3x/5) apples = (3x/5) * (6/3) = 6x/5 paise
3. The total cost of buying the apples = (3x/2) + (6x/5) = (15x + 12x)/10 = 27x/10 paise
4. The selling price of the apples = (30 * 100) + 30 = 3000 + 30 = 3030 paise
We know that you gained 24 paise, so:
Gain = Selling Price - Cost Price
24 = 3030 - (27x/10)
240 = 3030 - 27x
27x = 3030 - 240
27x = 2790
x = 2790 / 27
x = 103.333...
Since the number of apples cannot be a fraction, we need to round down to the nearest whole number. Therefore, you initially bought approximately 103 apples.