Word problems on Percentages

In this lesson, we will learn conversion of units from one into another and finally expressing them as percentages.

1. What percent of a kilometre is 100 meters?

We know 1 kilometre = 1000 meters.

Or 1 meter = 1/1000 km.

So, 100 meters = 100 × (1/1000) = 1/10 kms.

Now, convert fraction 1/10 into percent

1/10 = (1/10) × 100 % = 10%

Therefore, 100 metres is 10% of a kilometre.

2. An apple weighs 150 grams. What percent of a kilo it is?

1000 grams = 1 kilogram.

Therefore, 150 grams = 150/1000 = 15/100

Now, 15/100 is what percent?

It is (15/100) × 100 % = 15%

3. A bus travelled 8 kms. What distance did the bus travel as a percent of miles?

1 mile is 8/5 kilometres.

So 1 km is 5/8 miles and so, 8 kms is (5/8) × 8 = 5 miles.

So, what percent is 8 kms of 5 miles is the question

(8 kms/5 miles) ×100% = (5 miles/5miles) × 100% = 1 × 100% = 100%

4. To clear a test, a student must score 35% of 125 marks. How much should a student score to the nearest integer?

Now 35% of 125 is Round off this decimal number 43.75 to the nearest integer.

First round off hundredth digit 5 to tenth place.

After 5 is rounded off to tenth place, 7 should be increased by 1.

43.75 becomes 43.8

Next, round off tenth digit 8 to unit’s place 3.

After 8 is rounded off to unit’s place, increase 3 by 1.

43.8 becomes 44.

A student must therefore score 44 marks to clear the given test.

5. A staff is 3 feet long. How much percent it is of one metre?

1 feet = 30 cms and 1 metre = 100 cms.

3 feet long stick measure 3 × 30 = 90 cms.

Now, 90 cms is what percent of 100 cms. It is

90 per 100 is same 90/100 which is straight away 90%

6. A staff is 120 cms long. What percent of one metre is the staff?

120 is what percent of 100. Write it as

120/100 which is again 120%

7. An elephant consumes 120 litres of water every day. A tank can store only 85% of this volume. How much does the capacity of the tank fall short of?

85% of 120 is (85/100) × 120 = 102

Capacity of the tank is 102 litres.

Quantity of water consumed is 120 litres.

Therefore, deficit is 120 – 102 = 18 litres.

8. What percent does each of the following angles constitute out of 3600?

1. Acute angle

2. Right angle

3. Straight line angle

4. Reflex angle,

5. One full rotation of a straight line

Let us call each angle as x.

1. For acute angle,

0 < x < 900

In percentage terms, therefore

0% < x < (900/3600) × 100%

i.e.  0% < x < (¼) ×100%

0% < x < 25%

2. Right Angle is 900

To find what percent A is of B, find (A/B) ×100%

Therefore, 900 is what percent of 3600,

(900/3600) × 100% = (1/4) × 100% = 25%

3. Angle of a straight line is 1800

So, 1800 is what percent of 3600

It is, (180/360) × 100% = (1/2) × 100% = 50%

4. Reflex angle lies from 1800 to 2700

So, 1800< x < 2700

Express in percent terms as

(1800/3600) ×100% < x < (2700/3600) ×100%

(1/2) ×100% < x < (3/4) ×100%

50% < x < 75%

5. One full rotation of a straight line is 3600

What percent is 360 degrees out of 3600

(3600/3600) ×100% = 1 ×100% = 100%

9. In the number 1234 what percent is the place value of the digit 3 of the place value of the digit 2?

In the integer 1234, 3 is in ten’s place and 2 is in hundred’s place.

So the place value of 3 is 10, while that of 2 is 100.

Now we have to find, 10 is what percent of 100?

It is (10/100) ×100% = 10%

10. What percent of quadrilaterals have same sides?

The 6 quadrilaterals are irregular quadrilateral, trapezium, parallelogram, rhombus, rectangle and square

Among 6 quadrilaterals, 2 have all sides equal, namely rhombus and square.

Therefore, 2 out 6 have all sides equal in length.

2 out of 6 is what percent?

(2/6) ×100% = (1/3) ×100% = 33.33% or 