IBM and KTC quote for a tender. One the tender opening day, IBM realizes that their quotations are in the ratio `7 : 4` and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC's quoted price. KTC realizes that the final quotes of the two were in th ratio `3 : 4`. What was the price at which IBM won the bid?

Options

A. Rs 7 Lakh
B. Rs 4 Lakh
C. Rs 3 Lakh
D. Rs 1.5 Lakh

Answer

To solve the problem step by step, let's denote the initial quotations of IBM and KTC as follows:

1. **Initial Quotations**:
- Let the initial quotation of IBM be \( 7X \).
- Let the initial quotation of KTC be \( 4X \).

2. **Price Reduction**:
- IBM decreases its price to be Rs 1 lakh lower than KTC's quoted price. Thus, the final price of IBM becomes:
\[ \text{Final Price of IBM} = 4X - 1,00,000 \]

3. **Final Quotations Ratio**:
- After the negotiation, the final quotations of IBM and KTC are in the ratio \( 3 : 4 \). This can be expressed as:
\[ \frac{4X - 1,00,000}{4X} = \frac{3}{4} \]

4. **Cross Multiplying**:
- To eliminate the fraction, we cross-multiply:
\[ 4(4X - 1,00,000) = 3(4X) \]

5. **Expanding the Equation**:
- Expanding both sides gives:
\[ 16X - 4,00,000 = 12X \]

6. **Rearranging the Equation**:
- Rearranging the equation to isolate \( X \):
\[ 16X - 12X = 4,00,000 \]
\[ 4X = 4,00,000 \]
\[ X = 1,00,000 \]

7. **Calculating Final Prices**:
- Now, substituting \( X \) back to find the final price of IBM:
\[ \text{Final Price of IBM} = 4X - 1,00,000 = 4(1,00,000) - 1,00,000 = 4,00,000 - 1,00,000 = 3,00,000 \]

Thus, the price at which IBM won the bid is **Rs 3,00,000**.