Question : Reshma buys two articles A and B for Rs. 1,734. She sells A at a loss of 16% and sells B at a gain of 20%. The selling price of both articles is the same. If A is sold for Rs. 1,147.50, then the gain percent on A is:

Option 1: 12.5

Option 2: 12

Option 3: 10.5

Option 4: 10

Correct Answer: 12.5

Solution : Let, the cost price of articles A and B be A and B respectively
According to the question,
A + B = Rs. 1734................(1)
Loss % of A = 16%
Gain % of B = 20%
SP ₁ of A = SP ₁ of B
SP ₂ of A = Rs. 1,147.50
We know,
SP = CP × (100 + gain %)/100
SP = CP × (100 – Loss %)/100
Gain = SP – CP
Gain % = $\frac{Gain}{CP} × 100$
where SP is the selling Price and CP is the cost price.
⇒ SP ₁ of A = A × $\frac{100 – 16}{100}$
⇒ SP ₁ of A = 0.84A...............(2)
⇒ SP ₁ of B = B × $\frac{100 + 20}{100}$
⇒ SP ₁ of B = 1.2B...............(3)
Equating equations 2 and 3
⇒ 0.84A = 1.2B
⇒ A = $\frac{10\mathrm{B}}{7}$
Putting the value of A in equation 1,
⇒ $\frac{10\mathrm{B}}{7}$ + B = 1734
⇒ $\frac{17\mathrm{B}}{7}$ = 1734
⇒ CP of B = Rs. 714
⇒ A = 1734 – 714
⇒ CP of A = Rs. 1020
SP ₂ of A = Rs. 1147.50
Gain ₂ = SP ₂ – CP
= 1147.50 – 1020
= Rs. 127.5
Gain % = $\frac{Gain _2}{ CP} × 100$
⇒ $\frac{127.5}{1020} × 100$
= 12.5 %
Hence, the correct answer is 12.5.