General Mathematics

Question: The difference between compound interest and the simple interest earned on a sum of money at the end of `4` years is Rs.`256.40` To find out the sum, which of the following information given in the statement P and Q is/are necessary ? p: Amount of simple interest accrued after `4` years Q: Rate of interest per annum.
A
Only P is necessary

B
only Q is necessary

C
Either P or Q is necessary

D
Neither P or Q is necessary

E
Both P and Q is necessary

Note: To find out the sum we need rate, time and the difference between C.I. and S.I. So.Q is necessary.
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Question: The difference between the compound interest and simple interest earned at the end of second year on a sum of money at `10%`per annum is Rs. `20`.The sum is :
A
`Rs.4000`

B
`Rs. 2000`

C
`Rs. 1500`

D
Date inadequate

Note: Let the principal be Rs. x. Then, C.I`= [ x (1 + 10/100)^2` S.I.`= ((x xx 10 xx 2)/100)` `= x/5` :. (C.I) - (S.I) `= ((21x)/100 - x/5)` `= x/100` `:. x/100 = 20` `or x = 2000`
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Question: What number should be subtracted from each of the numbers `23, 30, 57` and `78`so that the remainders may be proportional ?
A
`4`

B
`5`

C
`6`

D
`7`

Note: Let `(23 - x)/(30 - x) = (57 - x)/(78 - x)`. `:. (23 - x)(78 - x) = (57 - x)(30 - x)` or `- 101x + 1794 = 1710 - 87x` `iff 14x = 84` `iff x = 6`.
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Question: Which of the following ratios is the greatest ?
A
`7 : 15`

B
`15 : 23`

C
`17 : 25`

D
`21 : 29`

Note: `7/(15) = 0.466`, `(15)/(23) = 0.652`, `(17)/(25) = 0.68` & `(21)/(29) = 0.724`. Clearly, `0.724`is greatest and hence `21 : 29` is greatest.
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Question: A sum of Rs.`12000` deposited at compound interest becomes double after `5` years. After `20` years it will become :
A
`Rs. 120000`

B
`Rs. 192000`

C
`Rs. 124000`

D
`Rs. 96000`

Note: `12000 xx (1 + R/100)^5` `= 24000 ⇒(1 + R/100)^5 = 2` `:. [(1 + R/100)^5]^4` `= 2^4 = 16` `or (1 + R/100)^20 = 16` `or P(1 + R/100)^20 = 16p` `or 12000(1 + R/100)^20` `= 16 xx 12000` `= 192000`.
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Question: Two whole numbers whose sum is `72` cannot be in the ratio :
A
`5 : 7`

B
`3 : 5`

C
`4 : 5`

D
`3 : 4`

Note: The sum of the ratio terms must divide `72` So, the ratio cannot be `3 : 4`.
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Question: If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors ?
A
`2 : 1`

B
`3 : 1`

C
`3 : 2`

D
`7 : 5`

Note: For dividing `12` into two whole numbers, the sum of the terms of the ratio must be a factor of `12`. So, they cannot be in the ratio `3 : 2`.
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Question: The ratio of two numbers is `3 : 4` and their sum is `420`. The greater of the two numbers is :
A
`175`

B
`200`

C
`240`

D
`315`

Note: Required number `= (420 xx 4/7)` `= 240`.
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Question: The ratio between two numbers is `3 : 4` and their `1`c.m is `180`. The first number is :
A
`60`

B
`45`

C
`20`

D
`15`

Note: Let the numbers be `3x`and `4x`. Then, their `1`c.m `= 12x`. Now, `12x = 180` `iff x = 15`. `:.`First number `= 45`.
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Question: The L.C.M. and H.C.F. of two numbers `x` and `y` are `l` and `h` repectively. Then,
A
`l : h = x : y`

B
`x : h = l : y`

C
`x : l = y : h`

D
`x : h = y : l`

Note: Product of numbers = Product of their H.C.F. & L.C.M. `:. xy = lh` `iff x/h = l/y` `iff x : h = l : y`.
1. Report

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Question: The difference between the compound interest and simple interest earned at the end of second year on a sum of money at `10%`per annum is Rs. `20`.The sum is :

Question: What number should be subtracted from each of the numbers `23, 30, 57` and `78`so that the remainders may be proportional ?

Question: Which of the following ratios is the greatest ?

Question: A sum of Rs.`12000` deposited at compound interest becomes double after `5` years. After `20` years it will become :

Question: Two whole numbers whose sum is `72` cannot be in the ratio :

Question: If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors ?

Question: The ratio of two numbers is `3 : 4` and their sum is `420`. The greater of the two numbers is :

Question: The ratio between two numbers is `3 : 4` and their `1`c.m is `180`. The first number is :

Question: The L.C.M. and H.C.F. of two numbers `x` and `y` are `l` and `h` repectively. Then,