Profit & Loss, Discount & Tax

Q1: Fill in the blanks:

i. _______ =\(\frac{\left(100+gain%\right)}{100}\times\) _______.

Answer: S.P. = \(\frac{(100 + \text{gain} \%)}{100} \times\) C.P.

ii. Discount is always allowed on the ________ price.

Answer: Marked

iii. ________ = M.P. – Discount.

Answer: Selling Price

iv. If the S.P of an article is \(\frac{6}{5}\) of its cost price, then the gain per cent is _______.

\[ \text{Gain\%} = \left(\frac{6}{5} – 1\right) \times 100 = \frac{1}{5} \times 100 = 20\% \] Answer: 20%

v. A shopkeeper incurs a _______ if he sells 15 articles at the cost price of 12 articles.

Let C.P. of 1 article = ₹1 ⇒ C.P. of 15 articles = ₹15
If he sells 15 articles at C.P. of 12 articles ⇒ S.P. = ₹12
Loss = ₹3 on ₹15 ⇒ Loss% = \(\frac{3}{15} \times 100 = 20\%\)
Answer: loss of 20%

Q2: Write true (T) or false (F):

i. Gain or loss is always reckoned on the S.P.

Answer: False (F)
Explanation: Gain or loss is always calculated on the Cost Price (C.P.), not the Selling Price (S.P.)

ii. If a shopkeeper buys an article for ₹75 and sells it for ₹100, then his gain is 25%.

Gain = ₹100 − ₹75 = ₹25
Gain% = \(\frac{25}{75} \times 100 = 33\frac{1}{3}\%\)
Answer: False (F)

iii. C.P. = \(\frac{100}{\left(100-loss%\right)}\times\) S.P.

Answer: True (T)
Explanation: This is the correct formula to find C.P. when loss% and S.P. are known.

iv. If no discount is given, then cost price becomes equal to selling price.

Answer: False (F)
Explanation: If no discount is given, the marked price equals the selling price, not necessarily the cost price.