A sells an article to Bat a gain of 20% and B sells it to C at a gain of 10% and C sells it to D at a gain of 12`1/2`% If D pays 29.70, A purchased the article for:

Options

A. Rs 40
B. Rs 10
C. Rs 20
D. Rs 30

Answer

To find out how much A purchased the article for, we can work backward from the selling price that D paid. Here are the steps to solve the problem:

### Step 1: Understand the Selling Price
D pays ₹29.70 for the article. This is the final selling price after all the transactions.

### Step 2: Calculate C's Selling Price
C sells the article to D at a gain of 12.5%. We can express this gain as a fraction:
- Gain = 12.5% = 12.5/100 = 1/8
- Selling Price (SP) = Cost Price (CP) + Gain
- Therefore, SP = CP × (1 + Gain) = CP × (1 + 1/8) = CP × (9/8)

Let CP of C be x. Then:
\[ 29.70 = x \times \frac{9}{8} \]
To find x (C's cost price), we rearrange:
\[ x = 29.70 \times \frac{8}{9} \]
Calculating this gives:
\[ x = 29.70 \times 0.8889 \approx 26.40 \]

### Step 3: Calculate B's Selling Price
B sells the article to C at a gain of 10%. This gain can be expressed as:
- Gain = 10% = 10/100 = 1/10
- Therefore, SP = CP × (1 + Gain) = CP × (1 + 1/10) = CP × (11/10)

Let CP of B be y. Then:
\[ 26.40 = y \times \frac{11}{10} \]
To find y (B's cost price), we rearrange:
\[ y = 26.40 \times \frac{10}{11} \]
Calculating this gives:
\[ y = 26.40 \times 0.9091 \approx 24.00 \]

### Step 4: Calculate A's Selling Price
A sells the article to B at a gain of 20%. This gain can be expressed as:
- Gain = 20% = 20/100 = 1/5
- Therefore, SP = CP × (1 + Gain) = CP × (1 + 1/5) = CP × (6/5)

Let CP of A be z. Then:
\[ 24.00 = z \times \frac{6}{5} \]
To find z (A's cost price), we rearrange:
\[ z = 24.00 \times \frac{5}{6} \]
Calculating this gives:
\[ z = 24.00 \times 0.8333 \approx 20.00 \]

### Conclusion
A purchased the article for ₹20.00.

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