Percent and Percentage — Exercise 9(D)

28% of a number is 84. Find the number.

Answer

Let the number be x.

$\Rightarrow \dfrac{28}{100} \times x = 84\\[1em] \Rightarrow x = \dfrac{84 \times 100}{28}\\[1em] \Rightarrow x = 300$

Hence, the required number = 300.

Every month, a man spends 72% of his income and saves ₹ 12,600. Find:

(i) his monthly income

(ii) his monthly expenses

Answer

Percentage of income spent = 72%.

Percentage of income saved = (100 − 72)% = 28%.

(i) Let his monthly income be ₹ x. Given, 28% of x = ₹ 12,600.

$\Rightarrow \dfrac{28}{100} \times x = 12,600\\[1em] \Rightarrow x = \dfrac{12,600 \times 100}{28}\\[1em] \Rightarrow x = 45,000$

So, his monthly income = ₹ 45,000.

(ii) Monthly expenses = income − savings = 45,000 − 12,600 = ₹ 32,400.

Hence, (i) his monthly income = ₹ 45,000 and (ii) his monthly expenses = ₹ 32,400.

1800 boys and 900 girls appeared for an examination. If 42% of the boys and 30% of the girls passed, find:

(i) number of boys passed

(ii) number of girls passed

(iii) total number of students passed

(iv) number of students failed

(v) percentage of students failed.

Answer

Number of boys = 1800 and number of girls = 900.

Total number of students = 1800 + 900 = 2700.

(i) Number of boys passed = 42% of 1800

$= \dfrac{42}{100} \times 1800$

= 756

Hence, the number of boys passed is 756.

(ii) Number of girls passed = 30% of 900

$= \dfrac{30}{100} \times 900$

= 270

Hence, the number of girls passed is 270.

(iii) Total number of students passed = 756 + 270 = 1026.

Hence, the total number of students passed is 1026.

(iv) Number of students failed = 2700 − 1026 = 1674.

Hence, the number of students failed is 1674.

(v) Percentage of students failed = $\left(\dfrac{1674}{2700} \times 100\right)$%

$= \dfrac{167400}{2700}$%

= 62%

Hence, the percentage of students failed is 62%.

$6\dfrac{1}{4}$% of a weight is 0.25 kg. What is 45% of this weight?

Answer

Let the weight be x kg.

As, $6\dfrac{1}{4}$% = $\dfrac{25}{4}$%

$\Rightarrow \dfrac{25}{4 \times 100} \times x = 0.25\\[1em] \Rightarrow \dfrac{25}{400} \times x = 0.25\\[1em] \Rightarrow x = \dfrac{0.25 \times 400}{25}\\[1em] \Rightarrow x = 4$

So, the weight = 4 kg.

Now, 45% of 4 kg = $\dfrac{45}{100} \times 4 = 1.8$ kg.

Hence, 45% of the weight = 1.8 kg.

An alloy consists of 13 parts of copper, 7 parts of zinc and 5 parts of nickel. Find the percentage of copper in the alloy.

Answer

Let the weight corresponding to each part be x kg.

So, copper = 13x, zinc = 7x and nickel = 5x.

Total weight of the alloy = 13x + 7x + 5x = 25x.

Percentage of copper = $\left(\dfrac{13x}{25x} \times 100\right)$%

$= \dfrac{1300}{25}$%

= 52%

Hence, the percentage of copper in the alloy = 52%.

An ore contains 15% of iron. How much ore will be required to get 36 kg of iron?

Answer

Let the quantity of ore required be x kg.

Given, 15% of the ore = 36 kg of iron.

$\Rightarrow \dfrac{15}{100} \times x = 36\\[1em] \Rightarrow x = \dfrac{36 \times 100}{15}\\[1em] \Rightarrow x = 240$

Hence, 240 kg of ore will be required.

Find the number which when increased by 6% becomes 424.

Answer

Let the number be x. When increased by 6%, it becomes 106% of x.

$\Rightarrow \dfrac{106}{100} \times x = 424\\[1em] \Rightarrow x = \dfrac{424 \times 100}{106}\\[1em] \Rightarrow x = 400$

Hence, the required number = 400.

Find the number which when decreased by 15% becomes 1360.

Answer

Let the number be x. When decreased by 15%, it becomes 85% of x.

$\Rightarrow \dfrac{85}{100} \times x = 1360\\[1em] \Rightarrow x = \dfrac{1360 \times 100}{85}\\[1em] \Rightarrow x = 1600$

Hence, the required number = 1600.

The cost of an article decreases from ₹ 17,000 to ₹ 15,980. Find the percentage decrease.

Answer

Original cost = ₹ 17,000 and new cost = ₹ 15,980.

Decrease in cost = 17000 − 15980 = ₹ 1020.

Percentage decrease = $\left(\dfrac{1020}{17000} \times 100\right)$%

$= \dfrac{102000}{17000}$%

= 6%

Hence, the percentage decrease = 6%.

Actual length of a rope is 22.5 m but it is wrongly measured as 21.6 m. Find the percentage error.

Answer

Actual length = 22.5 m and measured length = 21.6 m.

Error = 22.5 − 21.6 = 0.9 m.

Percentage error = $\left(\dfrac{\text{error}}{\text{actual length}} \times 100\right)$%

$= \left(\dfrac{0.9}{22.5} \times 100\right)$%

$= \dfrac{90}{22.5}$%

= 4%

Hence, the percentage error = 4%.