General Mathematics

Question: Two number are in the ration `3 : 5`. If each number is increased by `10`, the ratio becomes `5 : 7`. The numbers are:
A
`3, 5`

B
`12, 20`

C
`15, 25`

D
`18, 30`

Note: Let the numbers be `3x` and `5x`. `(3x + 10)/(5x + 10) = 5/7` `iff 7(3x + 10) = 5(5x + 10)` `iff x = 5`. So, the numbers are `15` and `25`.
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Question: What same number must be added to each term of the ratio `7 : 13` so that the ratio becomes `2 : 3` ?
A
`1`

B
`2`

C
`3`

D
`5`

Note: Let `x` be added. Then, `(7 + x)/(13 + x) = 2/3` `iff 3(7 + x) = 2(13 + x)` `iff x = 5`
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Question: What number should be subtracted from both the terms of the ratio `15 : 19` so as to make it as `3 : 4`?
A
`3`

B
`5`

C
`6`

D
`9`

Note: Let `x` be subtracted. Then, `(15 - x)/(19 - x) = 3/4` `iff 4(15 - x) = 3(19 - x)` `iff x = 3`.
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Question: The least whole number which when subtracted from the terms of the ratio `6 : 7` to give a ratio less than `16 : 21`, is :
A
`2`

B
`3`

C
`4`

D
`6`

Note: Let `x` be subtracted. Then, `(6 - x)/(7 - x) < (16)/(21)` `iff 21(6 - x) < 16(7 - x)` `iff 5x > 14` `iff x > 2.8` `:.` Least such number is `3`.
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Question: The ratio between two numbers is `3 : 4`. If each number is increased by `6`, the ratio becomes `4 : 5`. The difference between the numbers is :
A
`1`

B
`3`

C
`6`

D
`8`

Note: Let the numbers be `3x` and `4x`. Then, `(3x + 6)/(4x + 6) = 4/5` `iff 5(3x + 6) = 4(4x + 6)` `iff x = 6`. So, the numbers are `18` and `24`. `:.` Difference between the numbers `=(24 - 18)` `= 6`.
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Question: In how many years will a sum of Rs.`800`at `10%` per annum compounded semi - annually became Rs.`926.10 ?`
A
`2 1/2`

B
`1 1/2`

C
`2 1/3`

D
`1 1/3`

Note: Rate `= 5%` per half - year time= 2n half years = n years. Then, `800 (1 + 5/100)^2n` `= 926.10` `⇔ (21/20) = 926.10/800` `= 9261/8000` `= (21/20)^3`. `:. 2n = 3` `or n = 3/2 years`.
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Question: What number should be added to each of the numbers `8, 21, 13` and `31` so that the resulting numbers, in this order form a proportion ?
A
`2`

B
`3`

C
`5`

D
`7`

Note: Let `(8 + x)/(21 + x) = (13 + x)/(31 + x)`. Then, ` (8 + x)(31 + x) = (13 + x)(21 + x)` or `39x + 248 = 34x + 273` or `5x = 25` or ` x = 5`.
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Question: The present worth of Rs.`169` due in `2` years at `45` per annum compound interest is :
A
`Rs.150.50`

B
`Rs.154.75`

C
`Rs. 156.25`

D
`Rs. 158`

Note: Present worth `= Rs. [169/(1 + 4/100)]` `= Rs. (169 xx 25/26 xx 25/26)` `= Rs. 156.25`.
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Question: To find out the total compound interest accrued on a sum of money after `5` years, which of the following information given in the statements A and B is/are sufficient ? A: the rate of interest was `6%` per annum. B: The total simple interest on the same amount after `5` yaars at the same rate will be Rs.`600`
A
only A is sufficient

B
Either A or B is sufficient

C
Both A & B together are needed

D
Only A is sufficient

Note: Using A and B both, we may calculate : Sum`= ((100 xx 600)/(6 xx 5))` `= Rs. 2000`. So,the compound interest may be obtained. Thus, both A and B together are needed.
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Question: To find out the total compound interest accrued on a sum of money after `5` years, which of the folloeing informations given in the statements P and Q will be sufficient ? p: The sum was Rs.`2000` Q: The total amount of simple interest on the sum after `5` years was Rs. `4000`.
A
only P is sufficient

B
onlly Q is sufficient

C
Either P or Q is sufficient

D
Both P & Q are needed

E
Both P & Q are not sufficient

Note: Clearly, both A and Q are needed. Using P and Q, rate can be calculated as Rate`= ((100 xx 4000)/(5 xx 2000))` `= 4%` Now, C.I. can be calculated.
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Question: Two number are in the ration `3 : 5`. If each number is increased by `10`, the ratio becomes `5 : 7`. The numbers are:

Question: What same number must be added to each term of the ratio `7 : 13` so that the ratio becomes `2 : 3` ?

Question: What number should be subtracted from both the terms of the ratio `15 : 19` so as to make it as `3 : 4`?

Question: The least whole number which when subtracted from the terms of the ratio `6 : 7` to give a ratio less than `16 : 21`, is :

Question: The ratio between two numbers is `3 : 4`. If each number is increased by `6`, the ratio becomes `4 : 5`. The difference between the numbers is :

Question: In how many years will a sum of Rs.`800`at `10%` per annum compounded semi - annually became Rs.`926.10 ?`

Question: What number should be added to each of the numbers `8, 21, 13` and `31` so that the resulting numbers, in this order form a proportion ?

Question: The present worth of Rs.`169` due in `2` years at `45` per annum compound interest is :

Question: To find out the total compound interest accrued on a sum of money after `5` years, which of the folloeing informations given in the statements P and Q will be sufficient ? p: The sum was Rs.`2000` Q: The total amount of simple interest on the sum after `5` years was Rs. `4000`.