Test: Percentages - 1

Given:

The price of wheat is reduced by 4%.

Assumption:

Let the price of wheat be Rs.100/kg.

Calculation:

The price of 48 kg wheat  = 4800

As price is reduce by 4% it means that it became 96% of initial 100% hence,

After price decrease = 4800/96 = 50 kg

Hence, the required quantity of wheat = (50 – 48) = 2 kg more.

Given:

Difference between the 30% of a number and 22% of the same number = 4800

Calculation:

Let the number be P

According to the question,

30% of P – 22% of P = 4800

⇒ 8% of P = 4800

⇒ P = 60,000

And, 18% of P = (18/100) × 60,000 = 10,800

∴ 18% of P is 10,800

Given:

Kamal saves x% of her income 

Increase in his income = 26% 

Increase in his expenditure = 20% 

Increase in saving = 60% 

Concept used:

Income = Saving + Expenditure 

Calculations:

Let income of Kamal be 100 

Saving of Kamal = 100 × (x/100) = x

Expenditure of Kamal = 100 – x 

Kamal's salary after increment = 100 × (126/100) = 126

Kamal's expenditure after increment = (100 – x) × 120/100 = (100 – x) × 6/5 

New Saving = 126 – (100 – x) × 6/5      ----(1) 

New saving after increment = x × 160/100

New saving after increment = 8x/5      ----(2)

From eq. (1) and eq. (2)

⇒ 126 – (100 – x) × 6/5 = 8x/5 

⇒ 126 – 120 + 6x/5 = 8x/5

⇒ 6 = (8x/5) – (6x/5)

⇒ 6 = (8x – 6x)/5

⇒ 30 = 2x

⇒ x = 15

∴ The value of x is 15
Shortcut Trick:

Increase in AC = 6%

Increase in AC =

Decrease in CB = 5 - 3.18 = 1.82 cm

Decrease = 2 - 1.82 = 0.18 cm

So Percentage decrease 

Given:

Invalid votes = 20% of total votes

Percentage of votes candidate A gets = 54% of valid votes

The difference of votes in Candidates A and B = 3200

Concept used:

By using the concept of percentage

Calculation:

Let the total number of valid votes cast in the election be x.

Invalid votes = 20% of Total votes

Votes got by A = 54% of valid votes

⇒ Votes got by A = 54/100 × x

Votes got by B = (100% - 54%) of valid votes

⇒ Votes got by B = 46% of valid votes

⇒ Votes got by B = 46/100 × x

Required difference = Votes got by A – Votes got by B

⇒ 3200 = (54/100 × x) – (46/100 × x)

⇒ 3200 = 8/100 × x

⇒ x = 40000

Total valid votes = 40000

Total valid votes = 80% of total votes cast

⇒ 40000 = 80/100 × Total votes cast

⇒ Total votes = 50000

∴ The total votes cast in the election is 50000.

Calculation:

Quantity of sugar in solution = 800 × (40/100) = 320 gm

Let the quantity of sugar added be x gm.

According to the question

⇒ (320 + x)/(800 + x) = 60/100

⇒ (320 + x)/(800 + x) = 3/5

⇒ (320 + x) × 5 = 3 × (800 + x)

⇒ 1600 + 5x = 2400 + 3x

⇒ 5x – 3x = 2400 – 1600

⇒ x = 400 gm
Shortcut Trick:

40%        100%

        60%

    40 : 20

      2 : 1

2 unit = 800 g

1 unit = 400 g

Given:

The difference between the 41% of a number and 33% of that number is 960.

33.33% = 1 / 3

Calculation:

Suppose the number is N.

∴ 41% of N – 33% of N = 960

⇒ 8% of N = 960

⇒ N = (960 × 100) / 8

⇒ N = 12,000

According to question:

⇒ 33.33% of N = 1 / 3 of 12,000 = 4,000

Given:

Increase % in the price of sugar = 25% 

Formula used:

Expense = Price × Quantity 

Calculation:

Let the initial expenses on sugar was Rs.100

Now, the price rises by 25%

⇒ New price = (100 + 100 × 25%) = 125 

In order to keep the expense unaltered, Rs.25 has to be cut from Rs.125. 

⇒ 125 - 25 = 100 

∴ The decrease in the consumption = 25/125 × 100 = 20%
Alternate Method:

Reduction % = (Old quantity - New quantity)/Old quantity ×100

Let the price of 1 kg sugar = Rs.20 

Let the the quantity of sugar bought = 5 kg 

⇒ Expense = Price × Consumption = 20 × 5 = Rs.100

After increase of 25% in the price = Rs.20 × 125/100 = Rs.25

To keep the expense unchanged, that is Rs.100

⇒ New consumption = Rs.100/25 = 4 kg 

Reduce in the consumption = 5 kg - 4 kg = 1 kg 

∴ Percentage reduction in consumption = 1/5 × 100 = 20%
Shortcut Trick:

100 →  + 25% → 125 _____ - Y% → 100 

Now, Y = 25/125 × 100 = 20%

Given:

A student got 20% marks and failed by 72 marks. If he scores 40% marks then he gets 8 marks more than the passing marks. 

Concept:

Percentage.

Solution:

Let total marks be x

20% of total marks + 72 = 40% of total marks - 8

⇒ (20/100)x + 72 = (40/100)x - 8

⇒ (x/5) + 72 = (2x/5) - 8

⇒ x/5 = 80

⇒ x = 400 = total marks

Hence, passing marks

⇒ (x/5) + 72 = (400/5) +72

⇒ 152

∴ The passing marks is 152.

Let the third number = x

⇒ The first number = x - 50% of x = x/2

⇒ The second number = x - 75% of x = x/4

⇒ The percent by which second number has to be enhanced to make it equal to the first number = [(x/2 - x/4) / (x/4)] × 100 = 100%

(It can also be seen that x/4 is just half of x/2 so it has to be multiplied twice to become the second number which is 100%)

Alternate method

Let, 3rd number be 100

Hence, 2nd number will be 25 and 1st number will be 50

Now, 2nd number should be increased by 25 to make it equal to 1st number

∴ required percentage = 25/25 × 100 = 100%