Percentage and its Applications — Mental Maths

Fill in the blanks:

(i) Percentage is the numerator of a fraction with denominator .....

(ii) 15% of ..... is 135

(iii) $\dfrac{3}{4}$ = ..... %

(iv) 50 paise = .....% of 8 rupees

(v) A shopkeeper earns a profit if S.P. is ..... than C.P.

(vi) Loss or profit % is always calculated on ...... price.

(vii) The additional expenses on transportation, labour, repairing etc. are called ..... expenses.

(viii) Amount deducted from the marked price of an article is called .....

(ix) Discount = Marked price - ...... price

Answer

(i) Percentage is the numerator of a fraction with denominator 100.

(ii) Let the required number be $x$.

15% of $x$ = 135

$\Rightarrow \dfrac{15}{100} \times x = 135 \\[1em] \Rightarrow \dfrac{15x}{100} = 135 \\[1em] \Rightarrow x = \dfrac{135 \times 100}{15} \\[1em] \Rightarrow x = \dfrac{13500}{15} \\[1em] \Rightarrow x = 900$

Hence, 15% of 900 is 135.

(iii) $\dfrac{3}{4} = \dfrac{3}{4} \times 100$%

= $\dfrac{300}{4}$%

= 75%

Hence, $\dfrac{3}{4}$ = 75%.

(iv) Both the quantities must be in the same units.

8 rupees = (8 x 100) paise = 800 paise

Required percentage = $\dfrac{50}{800} \times 100$%

= $\dfrac{5000}{800}$%

= 6.25%

Hence, 50 paise = 6.25% of 8 rupees.

(v) A shopkeeper earns a profit if S.P. is more than C.P.

(vi) Loss or profit% is always calculated on cost price.

(vii) The additional expenses on transportation, labour, repairing etc. are called overhead expenses.

(viii) Amount deducted from the marked price of an article is called discount.

(ix) Discount = Marked price - selling price

State whether the following statements are true (T) or false (F):

(i) Discount is always calculated on marked price.

(ii) Two successive discounts of 20% and 20% are equivalent to single discount of 40%.

(iii) Overheads are always added to the original cost to get the total cost.

(iv) If S.P. is less than C.P. then shopkeeper suffers a loss.

(v) GST is always calculated on selling price.

Answer

(i) Discount is the amount deducted from the marked price of an article, so it is always calculated on the marked price.

Hence, the given statement is true.

(ii) Let the marked price of the article be ₹100.

S.P. after two successive discounts of 20% and 20% = $\Big(1 - \dfrac{20}{100}\Big)\Big(1 - \dfrac{20}{100}\Big) \times 100$

$= \dfrac{80}{100} \times \dfrac{80}{100} \times 100 \\[1em] = \dfrac{6400}{100} \\[1em] = ₹64$

Single discount = ₹100 - ₹64 = ₹36

Single discount percentage = $\dfrac{36}{100} \times 100$% = 36%

As 36% ≠ 40%, the two successive discounts of 20% and 20% are equivalent to a single discount of 36% and not 40%.

Hence, the given statement is false.

(iii) Overhead expenses such as transportation, labour and repairing charges are always added to the original cost to get the total cost.

Hence, the given statement is true.

(iv) When the selling price of an article is less than its cost price, the shopkeeper suffers a loss.

Hence, the given statement is true.

(v) GST is calculated on the selling price of an item and is added to the bill.

Hence, the given statement is true.