General Mathematics

Question: The average of first `50` natural numbers is :
A
`12.25`

B
`21.25`

C
`25`

D
`25.5`

Note: Sum of first n natural numbers `= (n(n + 1))/(2n)` `= (n + 1)/2` :. Average `= ((50 + 1)/2)` `= 51/2` `= 25 .5`
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Question: If `p : q = 3 : 4` and `q : r = 8 : 9`, then `p : r` is :
A
`1 : 3`

B
`3 : 2`

C
`2 : 3`

D
`1 : 2`

Note: `p/r = (p/q : q/r)` `= 3/4 xx 8/9` `= 2/3`. so, `p : r = 2 : 3`.
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Question: If `A : B = 8 : 15`, `B : C = 5 : 8` and `C : D = 4 : 5`, then `A : D` is equal to :
A
`2 : 7`

B
`4 : 15`

C
`8 : 15`

D
`15 : 4`

Note: `A/D = (A/B xx B/C xx C/D)` `= (8/15 xx 5/8 xx 4/5)` `= 4/ 15`. so, `A : D = 4 : 15`.
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Question: The ration `4^3.5 : 2^5` is the same as:
A
`4 : 1`

B
`2 : 1`

C
`7 : 5`

D
`7 : 10`

Note: `4^3.5 : 2^5 = (2^2)^(7/2) : 2^5` `= 2^7 : 2^5` `=2^2 : 1` `=4 : 1`. [Dividing each term by `2^5`]
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Question: If `15%`of `x` is the same as `20%` of `y` then `x : y` is :
A
`3 : 4`

B
`4 : 3`

C
`17 : 16`

D
`16 : 17`

Note: `15%` of `x = 20%` of, `y``iff``(15x)/100` `= (20y)/100``iff``x/y` `= 4/3`.
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Question: If `7 : x = 17.5 : 22.5`, then the value of `x` is :
A
`9`

B
`7.5`

C
`6`

D
`5.5`

Note: `7 xx 22.5 = x xx 17.5` `iff``x =(7 xx 22.5)/(17.5)` `iff``x = 9`.
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Question: If `1/5 : 1/x = 1/x : 1/(1.25)`, the value of `x` is :
A
`1.5`

B
`2`

C
`2.5`

D
`3.5`

Note: `1/5 xx 1/(1.25) = 1/x^2` `iff` `x^2 = 5 xx 1.25` `iff` `x^2 = 6.25` `iff` `x = 2.5`.
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Question: If `0.4 : 1.4 :: 1.4 : x`, the value of `x` is :
A
`49`

B
`4.9`

C
`0.49`

D
`0.4`

Note: `0.4 xx x = 1.4 xx 1.4` `iff` `x = (1.4 xx 1.4)/0.4` `= (14 xx 14)/40` `= 4.9`.
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Question: The compounded ration of `(2 : 3)`,`(6 : 11)` and `(11 : 2)`is :
A
`1 : 2`

B
`2 : 1`

C
`11 : 24`

D
`36 : 121`

Note: Required ratio `= 2/3 xx 6/11 xx 11/2` `= 2/1`, `= 2: 1`
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Question: If `2A = 3B = 4C`, then `A : B : C` is :
A
`2 : 3 : 4`

B
`4 : 3 : 2`

C
`6 : 4 : 3`

D
`3 : 4 : 6`

Note: Let `2A = 3B = 4C = k`. Then, `A = k/2`, `B = k/3` and `C = k/4`. `:. A : B : C = k/2 : k/3 : k/4` `= 6 : 4 : 3.`
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Question: The average of first `50` natural numbers is :

Question: If `p : q = 3 : 4` and `q : r = 8 : 9`, then `p : r` is :

Question: If `A : B = 8 : 15`, `B : C = 5 : 8` and `C : D = 4 : 5`, then `A : D` is equal to :

Question: The ration `4^3.5 : 2^5` is the same as:

Question: If `15%`of `x` is the same as `20%` of `y` then `x : y` is :

Question: If `7 : x = 17.5 : 22.5`, then the value of `x` is :

Question: If `1/5 : 1/x = 1/x : 1/(1.25)`, the value of `x` is :

Question: If `0.4 : 1.4 :: 1.4 : x`, the value of `x` is :

Question: The compounded ration of `(2 : 3)`,`(6 : 11)` and `(11 : 2)`is :

Question: If `2A = 3B = 4C`, then `A : B : C` is :