Percentage

Q1: Fill in the blanks

i. 240 ml is _______ % of 3l.

Step 1: Convert 3 litres = 3000 ml
Step 2: \[ \frac{240}{3000} \times 100 = 8\% \] Answer: 8%

ii. If x% of 35 is 42, then x = ______.

Step 1: \[ \frac{x}{100} \times 35 = 42 \\ \Rightarrow x = \frac{42 \times 100}{35} = 120 \] Answer: 120

iii. x% of y is y % of _______.

Step 1: \[ x\% \text{ of } y = y\% \text{ of } x \] Answer: x

iv. A period of 4 hours 30 min is _______ % of a day.

Step 1: Total minutes in 4 hrs 30 min = 270 min
Step 2: Total minutes in a day = 24 × 60 = 1440 min \[ \frac{270}{1440} \times 100 = 18.75\% \] Answer: 18.75%

v. The number which exceeds 20% of itself by 40, is ______.

Step 1: Let the number be \(x\) \[ x – \frac{20}{100}x = 40 \\ \Rightarrow \frac{80x}{100} = 40 \\ \Rightarrow x = \frac{40 \times 100}{80} = 50 \] Answer: 50

vi. If 24-carat gold is 100% pure, then the percentage of pure gold in 22-carat gold is ________.

Step 1: \[ \frac{22}{24} \times 100 = \frac{275}{3} = 91\frac{2}{3}\% \] Answer: \(91 \frac{2}{3}\)%

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

i. \(16\frac{2}{3}\%\) = 0.16

Step 1: Convert percentage to decimal: \[ 16\frac{2}{3}\% = \frac{50}{3}\% = \frac{50}{3 \times 100} = \frac{50}{300} \approx 0.1667 \] So, \(16\frac{2}{3}\% \ne 0.16\)
Answer: False (F)

ii. 5 g is 5% of 1 kg.

Step 1: 1 kg = 1000 g \[ 5\% \text{ of } 1000 = \frac{5}{100} \times 1000 = 50 \] So, 5 g is not 5% of 1 kg
Answer: False (F)

iii. If we double a number, we increase it by 100%.

Step 1: Let the number be \(x\)
Doubling: \(2x\); increase = \(2x – x = x\) \[ \text{Percentage increase} = \frac{x}{x} \times 100 = 100\% \] Answer: True (T)

iv. 36% when expressed as a ratio is equivalent to 9:50.

Step 1: \[ 36\% = \frac{36}{100} = \frac{9}{25} \] But \(9:50 \ne \frac{9}{25}\)
Answer: False (F)

v. If 26% of x = 65, then x = 250

Step 1: \[ \frac{26}{100} \cdot x = 65 \Rightarrow x = \frac{65 \cdot 100}{26} = 250 \] Answer: True (T)