Costs of two watches were in the ratio of 16:23. The cost of first watch increases by 10% and that of second by Rs. 477. Now the costs of two watches are in a ra tio of 11: 20. The price of the second watch (in Rs.) In the be ginning was

Options

A. 932
B. 1219
C. 1696
D. 848

Answer

To solve the problem step by step, we will denote the cost of the first watch as \( 16x \) and the cost of the second watch as \( 23x \), where \( x \) is a common factor.

### Step 1: Define the initial costs
Let:
- Cost of the first watch = \( 16x \)
- Cost of the second watch = \( 23x \)

### Step 2: Calculate the new cost of the first watch after a 10% increase
The cost of the first watch increases by 10%. Therefore, the new cost of the first watch is:
\[ \text{New cost of first watch} = 16x + 0.10 \times 16x = 16x \times 1.1 = 17.6x \]

### Step 3: Calculate the new cost of the second watch after an increase of Rs. 477
The cost of the second watch increases by Rs. 477. Therefore, the new cost of the second watch is:
\[ \text{New cost of second watch} = 23x + 477 \]

### Step 4: Set up the ratio of the new costs
According to the problem, the new costs of the watches are in the ratio of 11:20. Therefore, we can write the equation:
\[ \frac{17.6x}{23x + 477} = \frac{11}{20} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 20 \times 17.6x = 11 \times (23x + 477) \]
This simplifies to:
\[ 352x = 253x + 5247 \]

### Step 6: Solve for \( x \)
Now, we will solve for \( x \):
\[ 352x - 253x = 5247 \]
\[ 99x = 5247 \]
\[ x = \frac{5247}{99} = 53 \]

### Step 7: Calculate the initial cost of the second watch
Now that we have \( x \), we can find the initial cost of the second watch:
\[ \text{Cost of the second watch} = 23x = 23 \times 53 = 1219 \]

### Final Answer
The price of the second watch in the beginning was Rs. 1219.

---