Question 6

# Yayati sold an item at a loss of 13%. If he had sold it for ₹ 49 more, he would have made a profit of 22%. Whatshouldbe the selling price of the item to gain a profit of 30%?

Solution

Let take cost price=x

$$SP = [\frac{(100 - Loss \%)}{ 100}]\times(CP)$$

$$SP = [\frac{(100 - 13 )}{ 100}]\times(CP)$$

$$SP = [\frac{87}{ 100}]\times(CP)$$

$$SP =.87\times(CP)$$

Now if he sell it for 49 more

$$SP =.87\times(CP)+49$$  ..........eq 1

Profit will 22%

$$SP = [\frac{(100 + Gain\%)}{ 100}] \times CP$$

$$SP = [\frac{(100 + 22)}{ 100}] \times CP$$

$$SP =1.22 \times CP$$ ............ eq 2

SP in both equation same

eq 1=eq2

$$.87\times(CP)+49=1.22 \times CP$$

$$49=1.22 \times CP-.87\times(CP)$$

$$49=.35\times(CP)$$

$$\frac{49}{.35}=CP$$

$$CP=140$$

profit=30%

$$SP = [\frac{(100 + Gain\%)}{ 100}] \times CP$$

$$SP = [\frac{(100 + 30)}{ 100}] \times140$$

$$SP = [\frac{(130)}{ 100}] \times140$$

$$SP = 182$$