Question

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 loss or gain in the whole transaction. Find the individual cost prices of the two watches.​

Answer 1

Step-by-step explanation:

$\bigstar$ Given:-

• 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 loss or gain in the whole transaction.

$\bigstar$ To Find:-

• The individual cost prices of the two watches.

$\bigstar$ Solution:-

✇ Let the CP of 1st watch be Rs.x

✇ CP of 2nd watch = Rs. (13440 - x)

$\begin{array}{c | l} \: \sf \: \purple{For \: 1st \: watch }\sf & \sf \green{ \:For \: 2nd \: watch} \\ \\ \sf \: \therefore \: SP = \frac{100 + gain\%}{100} \times CP \: & \sf \: \therefore SP = \frac{100 - loss\%}{100} \times CP \\ \\ \\ = \sf \: ₹ \bigg( \frac{100 + 16}{100} \times x \bigg)\: & = ₹ \sf \: \: \bigg\{ \: \frac{100 - 12}{100} \times (13440 - x) \bigg\} \\ \\ \\ = \sf\: ₹ \bigg( \frac{116}{100} \times x \bigg) \: & = ₹ \sf\: \bigg\{ \frac{88}{100} \times (13440 - x) \bigg\} \\ \\ \\ = ₹ \bf \bigg( \frac{29x}{24} \bigg) \: & = ₹ \bf\bigg\{ \frac{22}{25} (13440 - x) \bigg\} \end{array}</strong></p><p></p><p><strong>[tex] \begin{array}{c | l} \: \sf \: \purple{For \: 1st \: watch }\sf & \sf \green{ \:For \: 2nd \: watch} \\ \\ \sf \: \therefore \: SP = \frac{100 + gain\%}{100} \times CP \: & \sf \: \therefore SP = \frac{100 - loss\%}{100} \times CP \\ \\ \\ = \sf \: ₹ \bigg( \frac{100 + 16}{100} \times x \bigg)\: & = ₹ \sf \: \: \bigg\{ \: \frac{100 - 12}{100} \times (13440 - x) \bigg\} \\ \\ \\ = \sf\: ₹ \bigg( \frac{116}{100} \times x \bigg) \: & = ₹ \sf\: \bigg\{ \frac{88}{100} \times (13440 - x) \bigg\} \\ \\ \\ = ₹ \bf \bigg( \frac{29x}{24} \bigg) \: & = ₹ \bf\bigg\{ \frac{22}{25} (13440 - x) \bigg\} \end{array}$

Since there is no loss or gain in the whole transaction, so, the combined SP of the two watches = combined CP of the two = ₹ 13440

$\tt \: \frac{29x}{25} + \frac{22}{25} (13440 - x) = 13440 \\ \\ \\ \: \twoheadrightarrow \tt \: 29x + 22(13440 - x) = 13440 \times 25 \\ \\ \\ \twoheadrightarrow \tt \: 7x + 13440 \times 22 = 13440 \times 25 \\ \\ \\ \twoheadrightarrow \tt \: 7x = 13440 \times (25 - 22) \\ \\ \\ \twoheadrightarrow \tt \: x = \frac{ \cancel{13440} \times 3}{ \cancel7 } \\ \\ \\ \large \boxed{ \underline{\color{indigo}{ \frak{x =₹ 5760}}}}$

❒ CP of 1st watch = ₹ 5760

❒ CP of 2nd watch = 13440 - 5760

⇨ ₹ 7680