Concept of Mathematics
Percentage
Word problems to calculate percent
Question: (151) What will be the number, if three fourth of the number is twelve less than eighty percent of the number?
Solution:
Let the number = 100
`:. 80%` of `100 = 80`
And ` 3/4 xx 100 = 75`
Now difference ` = 80-75=5`
If the difference is 5, then number = 100
∴ if the difference is 1, then number `=(100)/5 =20`
∴ if the difference is 12, then number `=20 xx 12 = 240`
Thus, required number = 240 Answer
Shortcut/Alternate Method
Let the number `=x`
`:. 80%` if `x - 3/4` of `x=12`
`=> (80x)/(100)-(3x)/4=12`
`=> (80x-75x)/(100)=12`
`=> 80x-75x = 1200`
`=> 5x = 1200`
`:. x = (1200)/5`
`=> x = 240` Answer
Question: (152) A quality control inspector rejects 0.2 percent of motorcycle as defective. If he found 50 motorcycle defective then how many he examined? (Similar question asked in SST, MAT)
Solution:
Given, `0.2%` motorcycle found defective
This means 0.2 motocyles found defective when 100 are inspected
∴ To find 1 motorcycle defective number of motorcycles to be inspected `=(100)/(0.2)`
∴ To find 50 motorcycle defective number of motorcycles to be inspected `= (100)/(0.2)xx 50`
`=(100 xx 50 xx 10)/2`
`= 25000` Answer
Shortcut/Alternate Method
Given, `0.2%` motorcycles rejected
Total number of motorcycles rejected = 50
Number of motorcycles inspected =?
Let number of motocyles to reject 50 of them `=x`
`:. 0.2% of x = 50`
`=> (0.2)/100 xx x = 50`
`=> x = (50 xx 100)/(0.2)`
`=> x = (50 xx 100 xx 10)/2`
`=> x = 25000` Answer
Question: (153) An inspector rejects 0.5 percent of TV sets as defective while examine. How many TV sets will be examined to reject 10 TV sets as defective. (Similar question asked in SST, MAT)
Solution:
Let total number of TV sets examined = 100
∴ Number of rejects TV sets `= 0.5% = 0.5`
Now, when 0.5 TV sets are rejected then number of sets examined = 100
∴ To reject 1 TV sets number of sets to be examined `=(100)/(0.5)`
∴ To reject 10 TV sets number of sets to be examined `=(100)/(0.5)xx10`
`=(100 xx 10 xx 10)/5`
`= 2000` TV sets Answer
Shortcut/Alternate Method
Let number of TV sets to be examined to reject 10 sets `=x`
`:. 0.5% of x = 10`
`=> (0.5)/(100)xx x=10`
`=>x = (10 xx 100)/(0.5)`
`=> x = (10 xx 100 xx 10)/5`
`=> x = 2000` Answer
Question: (154) How many articles to be examined to reject 4 as defective if an inspector rejects 0.08% of the articles inspected as defective?(Similar question asked in MAT, SST)
Solution:
Let the total number of articles examined = 100
∴ Number of rejected articles `= 0.08% = 0.08`
∵ To reject 0.08 articles total number of articles examined = 100
∴ To reject 1 article total number of articles examined `=(100)/(0.08)`
∴ To reject 4 articles total number of articles examined `=(100)/(0.08)xx4`
`=(100xx4xx100)/8 = 5000`
Shortcut/Alternate Method
Let total number of articles `= x`
`:. 0.08% of x = 4`
`=> (0.08)/(100)xx x = 4`
`=> x = (4xx100)/(0.08)`
`=> x = (4 xx 100 xx 100)/8`
`=> x = 5000` Answer
Question: (155) An inspector rejects 0.8% of the meters as defective. How many will be examined to reject 2? (MAT 2000)
Solution:
Let the total number of meters examined = 100
`:. 0.8%` of total meters `=100 xx 0.8 xx 1/(100)=08`
∵ To reject 0.8 meters number of meters examined `=100`
∴ To reject 1 meter number of meters to be examined `=(100)/(0.8)`
∴ To reject 2 meters number of meters to be examined `=(100)/(0.8)xx2`
`=(100 xx 2 xx 10)/8`
`=250` Answer
Shortcut/Alternate Method
Let total number of meters to be examined to reject `2 =x`
`:. 0.8%` of `x=2`
`=> (0.8)/(100)xx x =2`
`=> x = (2xx100)/(0.8)`
`=>x=(2xx100xx10)/8`
`=>x = 250` Answer
Question: (156) After increase in excise duty from `3 1/10%` to `7 1/10%` the price of a TV set will increase to how much percent?
Solution:
Given, old rate of excise duty `= 3 1/10% = 31/10%`
New rate of excise duty `= 7 1/10% = 71/10%`
Let the price of TV set `= Rs. 100.00`
`:.` Price of TV at old rate of excise duty `= Rs. 100 xx 31/10 xx 1/100`
`= Rs. 3.10`
Now, price of TV at old rate of excise duty `= Rs. 100 xx 71/10 xx 1/100`
`= Rs. 7.10`
`:.` Increase in price of TV `= Rs. 7.10 - Rs. 3.10`
`= Rs. 4.00`
Since, on Rs. 100 increase `=Rs. 4.00`
`:. Increase = 4% Answer`
Shortcut method
Effective increase in % = New rate of excise duty in % – Old rate of excise duty in %
`= 7 1/10% - 3 1/10%`
`= 71/10% - 31/10% = 40/10%`
` = 4% Answer`
Question: (157) Sales tax on petrol increased from `5%` to `8%`. If the marked price of petrol is Rs. 60.00 per liter how much more money David has to pay per week if he consumed 10 litres of petrol per day?
Solution:
Given, old rate of sales tax on petrol `= 5%`
New rate of sales tax on petrol `= 8%`
Marked price of petrol `= Rs. 60.00` per litre
Consumption of petrol per day by David `= 10 litre`
`:.` Consumption of petrol per week `= 10 xx 7 = 70 litre`
`:.` Effective price of petrol @ `5%` of sales tax
`= Rs. 60.00 + 60.00 xx 5/100`
`= Rs. 60.00 + 3.00 = Rs. 63.00`
Effective price of petrol at new rate i.e. `8%` of sales tax
`= Rs. 60.00 + 60.00 xx 8/100`
`= Rs. 60.00 + 4.80 = Rs. 64.80`
Price of petrol per week at old rate of sales tax `= Rs. 63.00 xx 70 = Rs. 4410.00`
Price of petrol per week at new rate of sales tax `= Rs. 64.80 xx 70 = Rs. 4536.00`
`:.` Increase in expenditure = price of petrol per week at new rate of sales tax `-` price of petrol per week at old rate of sales tax
`= Rs. 4536.00 - Rs. 4410.00 `
`= Rs. 126.00`Thus, David has to pay Rs. 126.00 more per week.
Shortcut method:
Increase in sales tax `= 8% - 5% = 3%`
`:.` increase in price on one litre of petrol `= Rs. 60 xx 3/100`
`= Rs. 1.80`
`:.` increase in price per week
`= Rs. 1.80 xx 10 xx 7`
`= Rs. 126.00 Answer`
Question: (158) If the sales tax is increased from 2`1/3`% to 2`1/2`%, then how much more money a person have to pay for an article with marked price of Rs. 6600.00?
Solution:
Sales tax for Rs. 6600.00 @ 2`1/3`%
= Rs. 6600.00 `xx` 2`1/3` `xx` `1/100`
= Rs. 66.00 `xx` `7/3`
= RS. 22.00 `xx` 7
= Rs. 154.00
Now, Salex tax for Rs. 6600.00 @ 2`1/2`%
= Rs. 6600.00 `xx` `5/2` `xx` `1/100`
= Rs. `(66.00 xx 5)/2`
= Rs. 33.00 `xx` 5
= Rs. 165.00
Thus, difference in price = Rs. 165.00 `-` 154.00
= Rs. 11.00 Answer
Thus, a person have to pay Rs. 11.00 more for increased sales tax.
Question: (159) If the sales tax be reduced from 3`1/2`% to 3`1/3`% then what difference does it make to a person who purchase an article with marked price of Rs. 8400.00?
Solution:
Given, marked price = Rs. 8400.00
∴ Sales tax @ of 3`1/2`% will be
= Rs. 8400.00 `xx` 3`1/2` `xx` `1/100`
= Rs. 84.00 `xx` `7/2` = 42 `xx` 7
= Rs. 294.00
And, sales tax @ of 3`1/3`%
= Rs. 8400.00 `xx` 3`1/3` `xx` `1/100`
= Rs. 84.00 `xx` `10/3`
= Rs. 28.00 `xx` 10
= Rs. 280.00
∴ Difference in price = Rs. 294.00 `-` Rs. 280.00
= Rs. 14.00 Answer