Question

5. A shirt was sold at a profit of 15%. If its cost had
been 5% less and it had been sold for 21 less,
then profit would have been 10%. Find the cost of
the shirt.
​

Answer 1

Let CP of Shirt=₹x

Profit=15%

$sp = cp + (cp \times profit) \\ \\ = x + (x \times 15\%) \\ \\ = x + (x \times \frac{15}{100} ) \\ \\ = x + \frac{3x}{20} \\ \\ = \frac{23x}{20}$

SP=₹23x/20

Now if CP is 5% less.

New CP=

$x - (x \times 5\%) \\ \\ =x - ( x \times \frac{5}{100}) \\ \\ =x - \frac{x}{20} \\ \\ = \frac{19x}{20}$

New CP will get 10 profit.

$sp = cp + (cp \times 10\%) \\ \\ sp = \frac{19x}{20} + ( \frac{19x}{20} \times \frac{10}{100} ) \\ \\ sp = \frac{19x}{20} + \frac{19x}{200} \\ \\ \frac{19x \times 10 + 19x}{ 200} \\ \\ \frac{190x + 19x}{200} \\ \\ = \frac{209x}{200}$

SP of New CP=209x/200

Now difference between 1st SP and New SP=₹21

$\frac{23x}{20} - \frac{209x}{200} = 21 \\ \\ \frac{23 \times 10x - 209x}{200} = 21 \\ \\ \frac{230x - 209x}{200} = 21 \\ \\ \frac{21x}{200} = 21 \\ \\ 21x =21 \times 200 \\ \\ x = 21 \times \frac{200}{21} \\ \\ x = 200$

Original Cost of Shirt=₹200

Explanation

See When Original CP get 15% profut.

Then CP is Deducted by 5% we get New CP.

New CP get 10%

When Original CP get 15% profit and New CP get 10% profit then margin or Difference Between their SP =21

Hence Answer=₹200

$\underline{\mathbf{\huge{Price=Rs.200}}}$