the CP of two watches taken together is 13440 by selling one at profit of 16% and the Rat loss of 12% there is no profit no loss in the whole transaction find the individual cost price of the two watches

Let the cost price of the two watches be \( x \) and \( y \), where:

- \( x \) is the cost price of the watch sold at a profit of 16%.
- \( y \) is the cost price of the watch sold at a loss of 12%.

We are given that:

1. \( x + y = 13440 \) (the total cost price of both watches).
2. The entire transaction results in no profit, no loss.

For the watch sold at a profit of 16%, the selling price is:
\[
\text{Selling price of } x = x + 0.16x = 1.16x
\]

For the watch sold at a loss of 12%, the selling price is:
\[
\text{Selling price of } y = y - 0.12y = 0.88y
\]

Since there is no profit or loss in the transaction, the total selling price must equal the total cost price:
\[
1.16x + 0.88y = 13440
\]

Now we have the system of equations:
1. \( x + y = 13440 \)
2. \( 1.16x + 0.88y = 13440 \)

Let's solve these equations step by step.

### Step 1: Solving for \( y \)
From the first equation \( x + y = 13440 \), we can express \( y \) as:
\[
y = 13440 - x
\]

### Step 2: Substitute into the second equation
Substitute \( y = 13440 - x \) into the second equation:
\[
1.16x + 0.88(13440 - x) = 13440
\]

### Step 3: Simplify and solve for \( x \)
\[
1.16x + 0.88 \times 13440 - 0.88x = 13440
\]
\[
1.16x + 11827.2 - 0.88x = 13440
\]
\[
(1.16x - 0.88x) + 11827.2 = 13440
\]
\[
0.28x + 11827.2 = 13440
\]
\[
0.28x = 13440 - 11827.2
\]
\[
0.28x = 1612.8
\]
\[
x = \frac{1612.8}{0.28}
\]
\[
x = 5760
\]

### Step 4: Find \( y \)
Now that we have \( x = 5760 \), substitute this back into \( y = 13440 - x \):
\[
y = 13440 - 5760 = 7680
\]

### Final Answer:
- The cost price of the first watch \( x \) is **5760**.
- The cost price of the second watch \( y \) is **7680**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do we calculate profit or loss percentages?
2. Can we find the selling prices of both watches?
3. How would this change if there were a net profit in the transaction?
4. What if both watches had been sold at a loss?
5. How do simultaneous equations help in solving cost price problems?

**Tip**: Always start by forming equations based on the conditions given in word problems.

The CP of two watches taken together is 13440. By selling one at a profit of 16% and the other at a loss of 12%, there is no profit, no loss in the whole transaction. Find the individual cost price of the two watches.

Find the individual cost prices of two watches with a combined cost price of 13440, sold at 16% profit and 12% loss, leading to no profit or loss overall. This detailed solution includes step-by-step algebraic calculations for Grades 9-12.

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