EXPRESS A NUMBER AS A PERCENTAGE OF ANOTHER

Express the first quantity as a percentage of the second :

Problem 1 :

10 km, 50 km

Solution :

Expressing 10 km of 50 km as fraction :

= 10/50

Converting as percentage :

= (10/50) × 100

= 20%

So, the answer is 20%.

Problem 2 :

€2, €8

Solution :

Expressing €2 of €8 as fraction :

= 2/8

Converting as percentage :

= (2/8) × 100

= (1/4) × 100

= 25%

So, the answer is 25%.

Problem 3 :

300 m, 0.7 km

Solution :

1 km = 1000 m

0.7 km = 0.7 ×1000 = 700 m

Expressing 300 m of 700 m as fraction :

= 300/700

Converting as percentage :

= (300/700) × 100

= 42.9%

So, the answer is 42.9%.

Problem 4 :

60 cents, $2

Solution :

$1 = 100 cents

$2 = 200 cents

Expressing 60 cents of 200 cents as fraction :

= 60/200

Converting as percentage :

= (60/200) × 100

= 30%

So, the answer is 30%.

Problem 5 :

8 months, 2 years

Solution :

1 year = 12 months

2 year = 24 months

Expressing 8 months of 24 months as fraction :

= 8/24

= 1/3

Converting as percentage :

= (1/3) × 100

= 33%

So, the answer is 33%.

Problem 6 :

50 g, 1.2 kg

Solution :

1 kg = 1000 g

1.2 kg = 1.2 × 1000 = 1200 g

Expressing 50 g of 1200 g as fraction :

= 50/1200

Converting as percentage :

= (50/1200) × 100

= 4.2%

So, the answer is 4.2%.

Problem 7 :

24 min, 2 hours

Solution :

1 hour = 60 minutes

2 hour = 120 minutes

Expressing 24 minutes of 120 minutes as fraction :

= 24/120

Converting as percentage :

= (24/120) × 100

= 20%

So, the answer is 20%.

Problem 8 :

0.5 m, 25 cm

Solution :

1 m = 100 cm

0.5 m = 50 cm

Expressing 50 cm of 25 cm as fraction :

= 50/25

Converting as percentage :

= (50/25) × 100

= 200%

So, the answer is 200%.

Problem 9 :

5 mg, 2 g

Solution :

1 mg = 0.001 g

5 mg = 0.005 g

Expressing 0.005 g of 2 g as fraction :

= 0.005/2

Converting as percentage :

= (0.005/2) × 100

= 0.25%

So, the answer is 0.25%.

Problem 10 :

3 weeks, 15 days

Solution :

1 week = 7 days

3 weeks = 7 × 3 = 21 days

Expressing 21 days of 15 days as fraction :

= 21/15

= 7/5

Converting as percentage :

= (7/5) × 100

= 140%

So, the answer is 140%.

Problem 11 :

The tail of the spider monkey is 64% of its length. What is the length of its tail?

Solution :

Length of monkey = 55 inches

Length of tail = 64% of 55

= (64/100) x 55

= 0.64(55)

= 35.2 inches

So, the height of the tail is 35.2 inches.

Problem 12 :

A family pays $45 each month for cable television. The cost increases 7%.

a. How many dollars is the monthly increase?

b. What is the new monthly cost?

Solution :

a)

Amount paid by each month for cable = $45

Cost increases = 7%

a)  Amount increase = 7% of 45

= 7/100 x 45

= 0.07 (45)

= 3.15

So, the amount increase is $3.15

b) Each month it is increase by $3.15

For a year = 12 months

Total increament for the year = 12(3.15)

= $37.8

Problem 13 :

How many minutes is 40% of 2 hours?

Solution :

1 hour = 60 minutes

2 hours = 2(60)

= 120 minutes

40% of 120 minutes

= 0.40(120)

= 48 minutes

Problem 14 :

How many inches is 78% of 3 feet?

Solution :

1 feet = 12 inches

3 feet = 3(12)

= 36 inches

78% of 36 inches

= 0.78(36)

= 28.08 inches

Approximately 28 inches.

Problem 15 :

A fruit bowl contains only apples and oranges. The ratio of apples to oranges is 2:3. What percentage of the fruits in the bowl are oranges?

Solution :

Ratio between apples and oranges = 2 : 3

Number of apples = 2x and number of oranges = 3x

Total number of fruits = 2x + 3x

= 5x

Quantity of oranges = 3x/5x

Converting into percentage = (3/5) ⋅ 100%

= 3 ⋅ 20%

= 60%

Problem 16 :

Ayobami can type 360 words in 8 minutes and Chayann can type 516 words in 12 minutes. Determine who types faster and by how many words per minute.

Solution :

Number of words by Ayobami can type = 360 words in 8 minutes

In 1 minute = 360/8

= 45 words

Number of words by  Chayann can type = 516 words in 12 minutes

in 1 minute = 516/12

= 43 words

Ayobami is typing faster by 2 words per minute.