SOLVING WORD PROBLEMS ON PERCENTAGES

Problem 1 :

What is the value of 3 1/3 % of 1.5 % of smallest six digit number?

Solution :

Smallest six digit number is 100000.

1.5 % of the smallest six digit number

= (1.5/100) × 100000

= 0.015 × 100000

= 1500

3 1/3 % of 1500 = 10/3%

= 3.3% × 1500

= (3.3/100) × 1500

= 0.033 × 1500

= 49.5

Problem 2 :

What percent of 2/7 is 1/35?

Solution :

Let ‘x’ be required percentage.

x% of 2/7 = 1/35

(x/100) of (2/7) = 1/35

2x/700 = 1/35

x/350 = 1/35

Using cross multiplication.

35x = 350

x = 350/35

x = 10

So, 10 per cent of 2/7 is 1/35.

Problem 3 :

If the C.P. of 6 articles is equal to the S.P. of 4 articles, find the gain percent?

Solution :

Let cost price of one article be ‘x’.

The cost price of 6 articles = 6x

Cost price of 6 articles = Selling price of 4 articles

The selling price of 4 articles = 6x (because cost price of 6 articles)

Gain = 6x - 4x ==> 2x

So, gain percent is 50%

Problem 4 :

If 40% of a number is 256, then what is the 25% of that number?

Solution :

Let x be the original number.

If 40% of a number x = 256

(40/100) × x = 256

(2/5) × x = 256

x = 256 × (5/2)

x = 1280/2

x = 640

So, 25% of a number is 640.

Problem 5 :

If x% of 25/2 is 150, then what is the value of x?

Solution :

If x% of 25/2 =150

(x/100) × (25/2) = 150

x/100 = 150 × (2/25)

x/100 = 300/25

x/100 = 12

x = 12 × 100

x = 1200

So, the value of x is 1200.

Problem 6 :

What percentage of n umbers from 1 to 30 has the digit 9 in the unit place?

Solution :

Total number of numbers from 1 to 30 = 30

Numbers which has 9 at the unit place.

9,19 and 29.

Total numbers = 3

Required Percentage = (3/30) ×100

= 10%

Problem 7 :

If the cost price is 25% of selling price, then find the profit percent?

Solution :

Let x be the selling price.

Profit % = (profit / cost price) x 100%

Profit = Selling price - cost price

So, profit per cent = 300%

Problem 8 :

In how much time would the simple interest on a certain sum be 0.125 times the Principal at 10% per annum?

Solution :

Simple interest = (Principle value × rate × time)/100

0.125P = (P × 10 × T)/100

0.125P = (P × T)/10

T = (10 × 0.125P)/P

T = 10 × 0.125

T = 1.25

T = 125/100

T = 5/4

1 year 3 months is the investment period.

Problem 9 :

A tank can hold 50 litres of water. At present, it is only 30% full. How many litres of water shall i put in the tank, so that it is 80% full?

Solution :

Capacity of tank = 50 litres of water.

Tank full of the water = 30%

= (30/100) × 50

= 15 litres

80% full of the water is

= (80/100) × 50

= 40 litres

Number of liters to be put = 40 – 15

= 25 litres

25 litres of water i need to put.

Problem 10 :

A 60 lit tank was full of oil. Ram used 40% of it and poured the rest into a 40 lit tank.

(i) What percent of the 40 lit tank was filled with oil?

(ii) If Ram used 3 lit of oil daily, what percent of oil in the 40 lit tank would be used in 10 days?

Solution :

Quantity of oil in tank = 60 litres

40% of it is used.

Quantity of oil used = 40% of 60 lit

Quantity of oil remaining = 40 lit

= (40/100) × 60

= 24 litres

(i) Quantity of oil left = 60 - 24 ==> 36

Percent of the 40 lit tank = (36/40) × 100

= 90%  

(ii) Every day he uses 3 lit of oil

Quantity of oil used in 10 days.

= 10 × 3

= 30 lit

Quantity of oil in the 40 lit tank = 36 liter.

Percent of oil in the 40 lit in the tank = (30/36) × 100%

= 83.3%

Problem 11 :

The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns $120 at a performance where 8 people attend.

i) How much money will the performer earn when 20 people attend a performance?

a) $960      b) $480     c) $300      d) $240

ii)  The performer uses 43% of the money earned to pay the costs involved in putting on each performance. The rest of the money earned is the performer’s profit. What is the profit the performer makes at a performance where 8 people attend?

a) $51.60      b) $57.00      c) $68.40      d) $77.00

Solution :

i)  Amount earned when 8 people attend = 120

Amount earned by 1 person = 120/8

= $15

Amount earned when 20 people were attending = 20(15)

= $300

So, option c is correct.

ii)  43% of 120

= 0.43(120)

= 51.6

So, option a is correct.