Question

What percentage is

(i) Rs 15 of Rs 120?
(ii) 36 minutes of 2 hours?
(iii) 8 hours of 2 days
(iv) 160 metres of 4 km?
(v) 175 mL of 1 litre?
(vi) 25 paise of Rs 4?

Answer 1

(i) Let x% of Rs 120 be Rs 15.
Then, Rs $\left(\frac{x}{100}\times 120\right)$ = Rs 15
⇒ $\left(\frac{6x}{5}\right)$ = 15
∴ x = $\left(\frac{15\times 5}{6}\right)\%$ = $\left(\frac{25}{2}\right)\%$ = 12.5%
Hence, 12.5% of Rs 120 is Rs 15.

(ii) Let x% of 2 h be 36 min.
Then, $\left(\frac{x}{100}\times 2\times 60\right)$ min = 36 min
⇒ $\left(\frac{120x}{100}\right)$ = 36
∴ x = $\left(\frac{36\times 100}{120}\right)\%$ = 30%
Hence, 30% of 2 h is 36 min.

(iii) Let x% of 2 days be 8 h.
Then, $\left(\frac{x}{100}\times 2\times 24\right)$ h = 8 h
⇒ $\left(\frac{48x}{100}\right)$ = 8
∴ x = $\left(\frac{8\times 100}{48}\right)\%$ = $16\frac{2}{3}\%$
Hence, $16\frac{2}{3}\%$ of 2 days is 8 h.

(iv) Let x% of 4 km be 160 m.
Then, $\left(\frac{x}{100}\times 4\times 1000\right)$ m = 160 m
⇒ 40x = 160
∴ x = $\left(\frac{160}{40}\right)\%$ = 4%
Hence, 4% of 4 km is 160 m.

(v) Let x% of 1 L be 175 mL.
Then, $\left(\frac{x}{100}\times 1\times 1000\right)$ mL = 175 mL
⇒ 10x = 175
∴ x = $\left(\frac{175}{10}\right)\%$ = 17.5%
Hence, 17.5% of 1 L is 175 mL.

(vi) Let x% of Rs 4 be 25 paise.
Then, $\left(\frac{x}{100}\times 4\times 100\right)$ paise = 25 paise
⇒ 4x = 25
∴ x = $\left(\frac{25}{4}\right)\%$ = $6\frac{1}{4}\%$
Hence, $6\frac{1}{4}\%$ of Rs 4 is 25 paise.