Percentages

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Percentage:


What is Percentage?

    Percent is made of two words per and cent. Meaning of percent is “per hundred”. Sign of percent is %. To express x% as a fraction we have x% = x/100
Thus, 20% = 20/100 = 1/5; 54% = 54/100 = 27/50, etc.
To express a/b as a percent: We have, a/b = (a/b * 100)%
Thus, ¼ = (1/4 * 100)% = 25%; 0.6 = 6/10 = 3/5 = (3/5 * 100)% = 60%

 

  • If the price of commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is
    (R/((100+R))*100)%
  • If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is
    (R/((100-R))*100)%
  • Results on Population – Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
    Population after n years = P(1- R/100)n
    Population n years ago = P/((1+ R/100) )n
  • Results on Depreciation – Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
    Value of the machine after n years = P(1- R/100)n
    Value of the machine n years ago = P/((1- R/100) )n

 

If A is R% more than B, then B is less than A by (R/((100+R))*100)%

If A is R% less than B, then B is more than A by (R/((100-R) )*100)%

 

1. 3.5 can be expressed in terms of percentage as:
A)    0.35%

B)    3.5%


C)    35%

D)    350%

E)    None of these

Explanation: Answer is D

3.5 = 35/10= (35/10*100)%= 350%

 

2. 78% of 270 + 14% of 110 – ? = 108

A)    156

B)    118

C)    168

D)    158

E)    None of these

Explanation: Answer is B

Let 78% of 270 + 14% of 110 – x = 108

Then, x = (78/100*270)+ (14/100*110)- 108=210.60+15.40-108=226-108=118

 

3. 20% of 1440 + ? = 25% of 880 + 120% of 750

A)    372

B)    842

C)    832

D)    1052

E)    None of these

Explanation: Answer is C

Let 20% of 1440 + x = 25% of 880 + 120% of 750

Then, x = 25% of 880 + 120% of 750 – 20% of 1440
= (25/100*880+ 120/100*750)- (20/100*1440)=220+900-288
= 1120 – 288 = 832

 

4. 270 candidates appeared for an examination, of which 252 passed. The pass percentage is:

A)    80%

B)    831/2%

C)    901/3%

D)    931/3%

E)    None of these

Explanation: Answer is D

Pass percentage = ((252/270)*100)%=280/3%=93 1/3%

 

5. What percent of 7.2 kg is 18gms?

A)    .025%

B)    .25%

C)    2.5%

D)    25%

E)    None of these

Explanation: Answer is B

Required percentage = ((18/7200)*100)%= 1/4%=0.25%