Percentage, General Mathematics

Question: Prices register an increase of `10%` on food grains and `15%` on other items of expenditure. If the ratio of an employee's expenditure on food grains and other items be `2 : 5`, by how much should his salary be increased in order that he may maintain the same level of consumption as before, his present salary being `Rs. 2590 ?`
A
`Rs. 323.75`

B
`Rs. 350`

C
`Rs. 360.50`

D
None

Note: Let expenditure on food grains and other items be Rs. 2x and Rs. 5x. `2x + 5x = 2590` `or x = 370.` `:. F = 2 xx 370` `= 740, 0 = 5 xx 370` `= 1850.` New expenditure `= 110% of 740 + 115% of 1850.` `= (110/100 xx 740 + 115/100 xx 1850)` `= Rs. (814 + 2127.50)` `= Rs. 2941.50.`
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Question: The population of a town increases by `15%` annually. If its population was `8000` in `1995`, what will it be in `1997` ?
A
`9200`

B
`10400`

C
`9600`

D
`10580`

Note: Population in `1997 = 8000 xx (1 + (15)/(100))^2` `= (8000 xx (23)/(20) xx (23)/(20))` `= 10580`.
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Question: The population of a town is `18000`. It increases by `10%` during first year and by `20%` during the second year. The population after `2` years will be :
A
`19800`

B
`21600`

C
`23760`

D
None

Note: Required population `= 18000 xx (1 + (10)/(100)) xx (1 + (20)/(100))` `= (18000 xx (11)/(10) xx 6/5)` `= 23760`.
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Question: The value of a sewing machine depreciates every year by `4%`. Its value at present is `Rs 200`. What will be its value after `2` years ?
A
`Rs. (200 xx (23)/5)`

B
`Rs. [(200 xx (24)/(25))^2]`

C
`Rs. [200 xx ((25)/(26))^2]`

D
`Rs. [(200 xx (26)/(25))^2]`

Note: value after `2` years `= Rs. [200 xx (1 - 4/(100))^2]` `= Rs. [200 xx ((24)/(25))^2]`
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Question: The population of a city increases at the rate of `5%` annually. Its present population is `1,85,220`. Its population `3` years ago was :
A
`181500`

B
`183433`

C
`160000`

D
`127783`

Note: Population `3` years ago `= (185220)/(1 + (5/(100))^3` `= (185220 xx (20)/(21) xx (20)/(21) xx (20)/(21))` `=160000`.
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Question: The value of a machine depreciates at the rate of `10%` every year. It was purchased `3` years ago. If its present value is `Rs. 8748`, its purchase price was :
A
`Rs. 10000`

B
`Rs. 11372.40`

C
`Rs. 12000`

D
None

Note: `P xx (1 - (10)/(100))^3 = 8748` `=> P = (8748 xx (10)/9 xx (10)/9 xx (10)/9)` `= Rs. 12000`.
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Question: A ball pen factory decided to reduce its production by `10%` over that of previous month for next `3` months starting from February `1994`. In January `1994`, it produced `3000` ball pens. How many ball pens were produced in March `1994` ?
A
`2700`

B
`2430`

C
`2187`

D
`2400`

Note: Required number `= 3000 xx (1 - (10)/(100))^2` `= 3000 xx 9/(10) xx 9/(10)` `= 2430`.
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Question: The present population of a country estimated to be `10` crores is expected to increase to `13.31` crores during the next three years. The uniform rate of growth is :
A
`8%`

B
`12.7%`

C
`10%`

D
`15%`

Note: `10 "crores" xx (1 + R/(100))^3` `= 13.31 "crores"`. `:. (1 + R/(100))^3` `= (13.31 "crores")/(10 "crores")` `= (13.31)/(10)` `= (1331)/(1000)` `= ((11)/(10))^3`. So, `(1 + R/(100))` `= (11)/(10)` or `= R/(100)` `=((11)/(10) - 1)` `= 1/(10)` or `R = 10`.
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Question: A building worth `Rs 133, 100` is constructed on land worth `Rs. 72,900`. After how many years will the value of both be the same if land appreciates at `10%` p.a. and building depreciates at `10%` p.a. ?
A
`2 1/2`

B
`2`

C
`1 1/2`

D
`3`

Note: `72900 (1 + (10)/(100))^n` `= 133100 xx (1 - (10)/(100))^n` `:. ((11)/(10))^n xx ((10)/9)^n` `= (133100)/(72900)` `= (1331)/(729)` `:. ((11)/9)^n` `= ((11)/9)^3` `=> n` `= 3`.
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Question: The population of a town increases `4%` annually but is decreased by emigration annually to the extent of (1 / 2)%. What will be the increase percent in `3` years ?
A
`9.8`

B
`10`

C
`10.5`

D
`10.8`

Note: Let original population `= 100`. Population after `3` years `= 100 xx (1 + (31/2)/(100))^3` `= 100 xx (207)/(200) xx (207)/(200) xx (207)/(200)` `= 110.87`. `:.` Increase `% = 10.8%`.
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Question: The population of a town increases by `15%` annually. If its population was `8000` in `1995`, what will it be in `1997` ?

Question: The population of a town is `18000`. It increases by `10%` during first year and by `20%` during the second year. The population after `2` years will be :

Question: The value of a sewing machine depreciates every year by `4%`. Its value at present is `Rs 200`. What will be its value after `2` years ?

Question: The population of a city increases at the rate of `5%` annually. Its present population is `1,85,220`. Its population `3` years ago was :

Question: The value of a machine depreciates at the rate of `10%` every year. It was purchased `3` years ago. If its present value is `Rs. 8748`, its purchase price was :

Question: A ball pen factory decided to reduce its production by `10%` over that of previous month for next `3` months starting from February `1994`. In January `1994`, it produced `3000` ball pens. How many ball pens were produced in March `1994` ?

Question: The present population of a country estimated to be `10` crores is expected to increase to `13.31` crores during the next three years. The uniform rate of growth is :

Question: A building worth `Rs 133, 100` is constructed on land worth `Rs. 72,900`. After how many years will the value of both be the same if land appreciates at `10%` p.a. and building depreciates at `10%` p.a. ?

Question: The population of a town increases `4%` annually but is decreased by emigration annually to the extent of (1 / 2)%. What will be the increase percent in `3` years ?