Percentage — Mental Maths

Fill in the blanks:

(i) 25% of ................. = 45

(ii) 15% of ₹ ................. = ₹ 9

(iii) 8% of ................. kg = 480 g

(iv) 2% of ................. km = 100 m

(v) 9% of ................. m = 18 cm

Answer

(i) Let 25% of x = 45.

$\Rightarrow \dfrac{25}{100} \times x = 45\\[1em] \Rightarrow x = \dfrac{45 \times 100}{25}\\[1em] \Rightarrow x = 180$

Hence, 25% of 180 = 45.

(ii) Let 15% of ₹ x = ₹ 9.

$\Rightarrow \dfrac{15}{100} \times x = 9\\[1em] \Rightarrow x = \dfrac{9 \times 100}{15}\\[1em] \Rightarrow x = 60$

Hence, 15% of ₹ 60 = ₹ 9.

(iii) Let 8% of x kg = 480 g.

We know, 480 g = $\dfrac{480}{1000}$ kg = 0.48 kg.

$\Rightarrow \dfrac{8}{100} \times x = 0.48\\[1em] \Rightarrow x = \dfrac{0.48 \times 100}{8}\\[1em] \Rightarrow x = 6$

Hence, 8% of 6 kg = 480 g.

(iv) Let 2% of x km = 100 m.

We know, 100 m = $\dfrac{100}{1000}$ km = 0.1 km.

$\Rightarrow \dfrac{2}{100} \times x = 0.1\\[1em] \Rightarrow x = \dfrac{0.1 \times 100}{2}\\[1em] \Rightarrow x = 5$

Hence, 2% of 5 km = 100 m.

(v) Let 9% of x m = 18 cm.

We know, 18 cm = $\dfrac{18}{100}$ m = 0.18 m.

$\Rightarrow \dfrac{9}{100} \times x = 0.18\\[1em] \Rightarrow x = \dfrac{0.18 \times 100}{9}\\[1em] \Rightarrow x = 2$

Hence, 9% of 2 m = 18 cm.

Fill in the blanks:

(i) 175 g is ................. % of 2.5 kg.

(ii) $\dfrac{3}{5}$ expressed as percentage is ................. %.

(iii) If 6% of x is 0.21, then x = ................. .

(iv) Renu obtained 57 marks out of 150. She got ................. % marks.

(v) When ₹ 80 is increased by 15%, we get ₹ ................. .

(vi) ₹ 120 decreased by 15% = ₹ ................. .

Answer

(i) We know, 2.5 kg = 2500 g.

Required percentage = $\left(\dfrac{175}{2500} \times 100\right)$%

= $\dfrac{17500}{2500}$%

= 7%

Hence, 175 g is 7% of 2.5 kg.

(ii) To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\dfrac{3}{5} = \left(\dfrac{3}{5} \times 100\right)$%

= $\dfrac{300}{5}$%

= 60%

Hence, $\mathbf{\dfrac{3}{5}}$ expressed as percentage is 60%.

(iii) 6% of x = 0.21

$\Rightarrow \dfrac{6}{100} \times x = 0.21\\[1em] \Rightarrow x = \dfrac{0.21 \times 100}{6}\\[1em] \Rightarrow x = \dfrac{21}{6}\\[1em] \Rightarrow x = 3.5$

Hence, if 6% of x is 0.21, then x = 3.5.

(iv) Percentage of marks = $\left(\dfrac{57}{150} \times 100\right)$%

= $\dfrac{5700}{150}$%

= 38%

Hence, Renu got 38% marks.

(v) Increase = 15% of ₹ 80

= $\dfrac{15}{100} \times 80$

= ₹ 12.

Increased amount = ₹ (80 + 12) = ₹ 92.

Hence, when ₹ 80 is increased by 15%, we get ₹ 92.

(vi) Decrease = 15% of ₹ 120

= $\dfrac{15}{100} \times 120$

= ₹ 18.

Decreased amount = ₹ (120 − 18) = ₹ 102.

Hence, ₹ 120 decreased by 15% = ₹ 102.

Write (T) for true and (F) for false for each of the following statements:

(i) 0.023 = 2.3%

(ii) Per cent means out of 100

(iii) 5% of 1 cm = 5 mm

(iv) 123% = 12.3

(v) 8% = 0.8

Answer

(i) 0.023 = (0.023 × 100)% = 2.3%.

Hence, the statement is true (T).

(ii) By definition, per cent means per hundred or out of 100.

Hence, the statement is true (T).

(iii) We know that,

1 cm = 10 mm

5% of 1 cm = $\dfrac{5}{100} \times 10$ mm = 0.5 mm ≠ 5 mm.

Hence, the statement is false (F).

(iv) 123% = $\dfrac{123}{100}$ = 1.23 ≠ 12.3.

Hence, the statement is false (F).

(v) 8% = $\dfrac{8}{100}$ = 0.08 ≠ 0.8.

Hence, the statement is false (F).