EXPRESS THE FIRST QUANTITY AS A PERCENTAGE OF THE SECOND

Expressing one quantity as a percentage of another quantity :

Example 1 :

10 km,  50 km

Solution :

Step 1 :

Given quantities are in same unit.

Step 2 :

Express it as fraction.

=  (10/50)

Step 3 :

Convert the fraction as percentage.

=  (10/50) × 100%

=  (100/5)%

=  20%

So, 10 km is 20% of 50 km.

Example 2 :

€2, €8

Solution :

Both quantities are in same unit.

By expressing it as fraction, we get 2/8. Now converting it into percentage,

=  (2/8) × 100%

=  (100/4)%

=  25%

So, €2 is 25% of €8.

Example 3 :

300 m,   0.7 km

Solution :

We need both same units, so change from km to meter.

1 km  =  1000 m

0.7 km  =  0.7 × 1000

=  700 m

=  (300/700) × 100%

=  (3/7) × 100%

=  (300/7)%

=  42.86%

So, 300 m is 42.86% of  0.7 km.

Example 4 :

60 cents,   $2

Solution :

We need both in same unit, so change dollar as cents

1 dollar  =  100 cents

2 dollar  =  200 cents

=  (60/200) × 100%

=  (3/10) × 100%

=  30%

So, 60 cents is 30% of $2.

Example 5 :

8 months, 2 years

Solution :

We need both in same unit, so change year as month

1 year  =  12 months

2 years  =  24 months

=  (8/24) × 100%

=  (100/3)%

=  33 1/3%

So, 8 months is 33  1/3% of 2 years.

Example 6 :

50 g, 1.2 kg

Solution :

We need both same in units, so change kilogram as gram.

1 kg  =  1000 gram

1.2 kg  =  1200 g

=  (50/1200) × 100%

=  (0.04166) × 100%

=  4.17%

So, 50 g is 4.17% of 1.2 kg.

Example 7 :

24 min, 2 hours

Solution :

1 hour  =  60 min

2 hours  =  120 min

=  (24/120) × 100%

=  (0.2 × 100)%

=  20%

So, 24 min is 20% of 2 hours.

Example 8 :

0.5 m,  25 cm

Solution :

Both are not in same units, so change m to cm

1 cm  =  0.01 m

25 cm  =  0.25 m

=  (0.5/0.25) × 100%

=  (2 × 100)%

=  200%

So, 0.5 m is 200% of 25 cm.

Example 9 :

5 mg, 2 g

Solution :

Converting mg to grams, we get

1 gram  =  1000 milligram

2 g  =  2000 mg

=  (5/2000) × 100%

=  (0.0025 × 100)%

=  0.25%

So, 5 mg is 0.25% of 2 g.

Example 10 :

3 weeks, 15 days

Solution :

The quantities are not in the same unit. By converting them as days.

1 week  =  7 days

3 weeks  =  3(7)  ==>  21 days

=  (21/15) × 100%

=  (1.399 × 100)%

=  139. 9%

=  140%

So, 3 weeks is 140% of 15 days.

Example 11 :

For every 50 students at Hightown School, 29 are girls.

(a) Work out 29 as a percentage of 50.

1000 students attend Hightown School.

(b) How many girls attend Hightown School?

Solution :

a)  = 29/50

Converting as percentage,

= (29/50) x 100%

= 58%

When number of students is 1000.

= 58% of 1000

= 0.58(1000)

= 580

Example 12 :

A man earns $6000 in a month. If he spends $4000, what percent of his income does he save in a month?

Solution :

Amount he earns = $6000

Amount he spends = $4000

Percentage of income = (4000/6000) x 100%

= 66.6%

Example 13 :

Susan brings 500 flapjacks to a local fair. Susan sells 450 of the flapjacks. What percentage of the flapjacks did Susan sell?

Solution :

Number of flapjacks = 500

Number of flag jacks sells = 450

Percentage of flag jacks she sells

= (450/500) x 100%

= 0.9 x 100%

= 90%

Example 14 :

• James scored 30 out of 90 in a music test.
• He scored 48 out of 150 in a drama test.
• James scored 35 out of 120 in an art test.

In which test did James score the highest percentage? You must show your workings.

Solution :

Percentage in music test = (30/90) x 100%

= 33.3%

Percentage in drama test = (48/150) x 100%

= 32%

Percentage in music test = (35/120) x 100%

= 29.1%

Example 15 :

Sunil obtained 750 marks out of 800 and Ravi obtained 540 marks out of 600.Whose performance is better ?

Solution :

Percentage obtained by Sunil = (750/800) x 100%

= 0.9375 x 100%

= 93.75%

Percentage obtained by Ravi = (540/600) x 100%

= 0.9 x 100%

= 90%

So, Sunil's performance is better.

Example 16 :

A student spends 7 1/2 hours out of 24 hours at school. What percentage of the day does he spend in school ?

Solution :

Time spends = 7 1/2 hours

Total number of hours = 24

Percentage = [(15/2) / 24] x 100%

= 0.3125 x 100%

= 31.25%

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