General Mathematics

Question: A man invests a certain sum of money at `6%` p.a.simple interest and another sum at `7%`p.a. simple interest.His income from interest after `2` years was Rs.`354`. One fourth of the first sum is equal to one fifth of the second sum. The total sum invested was :
A
`Rs. 2600`

B
`Rs. 2700`

C
`Rs. 2880`

D
`Rs. 2900`

Note: Let the sums be x. and y. `(x xx 6 xx 2)/100 + (y xx 7 xx 2)/100 = 354` `or 6x + 7y = 17700` Also,` x/4 = y/5` `or 5x - 4y = 0` Solving thes equation we get : x `= x = 1200 and y = 1500` :. Total sum `= Rs. 2700`
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Question: what should be the least number of years in which the simple interest on Rs. `2600` at `6 2/3%` will be an exact number of rupees ?
A
`2`

B
`3`

C
`4`

D
`5`

Note: S.I. = Rs. (2600 xx 20/3 xx 1/100 xx T)` `= Rs. (520/3 xx T)`, which is an exact number of rupees when T `= 3`
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Question: A man invested `1/3` of his capital at `75 ; 1/4` at `8%` and the remainder at `10%`. If his annual income is Rs.`561`, the capital.
A
`Rs. 5400`

B
`Rs. 6000`

C
`Rs. 6600`

D
`Rs. 7200`

Note: Let total capital be x.Then, (x/3 xx 7/100 xx 1) + (x/4 xx 8/100 xx 1) + ((5x)/12 xx 10/100 xx 1)` `= 561` `or (7x)/300 + x/50 + x/24` `= 561` `or 51x = (561 xx 600)` `or x = ((561 xx 600)/51)` `= 6600`.
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Question: A man invests an amount of Rs. `15860` in the name of his three sons A,B and C in such a way that they get the same amount after `2,3` and `4` years respectively. If the rate of simple interest is `5%` then the ratio of amounts invested among A,B and C will be :
A
`10 : 15 : 20`

B
`22 : 23 : 24`

C
`6 : 4 : 3`

D
`2 : 3 : 4`

Note: Let the amounts invested be x.y.z. respectively. Then,`(x xx 2 xx 5)/100` `= y xx 3 xx 5)/100` `= (z xx 4 xx 5)/100` `= k` :. x = 10k, y = 20/3 k & z = 5k`. So,` x : y : z = 10k : 20/3 k : 5k` `= 30 : 20 : 15` `= 6 : 4 : 3`.
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Question: A man lends Rs. `10000` in four parts. If he gets `8%` on Rs. `2000 ; 7 1/2%` on Rs. `4000` and `8 1/2%`on Rs. `1400 ;` what percent must he get for the remainder, If his average annual interest is `8 : 13% ?`
A
`10 1/2%`

B
`9 1/4%`

C
`9%`

D
`7%`

Note: `((2000 xx 8 xx 1)/100) + (4000 xx 15/2 xx 1/100) + (1400 xx 17/2 xx 1/100) + 2600 xx R xx 1/100` `= 813/10000 xx 10000`. `or 160 + 300 + 119 + 26R` `= 813` `or R = 9`.
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Question: Rs.`2189` are divided into three parts such that their amounts after `1,2` and `3` years respectively may be equal, the rate of simple interest being `4%` p.a. in all case. The smallest part is ;
A
`Rs. 702`

B
`Rs. 597`

C
`Rs. 756`

D
`Rs. 1093`

Note: Let these part be x.y and `[2189 - (x + y)`.Then, `(x xx 1 xx 4)/100` `= (y xx 2 xx 4)/100` `= ([2189 - (x + y)] xx 3 xx 4)/100` `:. x/y = 2` `or x = 2y` `:. (2y xx 1 xx 4)/100` `= ((2189 - 3y) xx 3 xx 4)/100` `or 44y = 2189 xx 12`. `:. y = ((2189 xx 12)/44)` `= 597` :. Smallest part`= Rs. 597`.
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Question: The rates of interest in two banks A and B are inthe ratio `5 : 4. A person wants to deposit his total savings in two in such a way that he received equal fafl yearly interest from both. He should deposit the savings in banks A and B in the ratio :
A
`2 : 5`

B
`4 : 5`

C
`5 : 2`

D
`5 : 4`

Note: Let the savings be X and Y and the rates of simple interest be `5x` and `4x` respectively. Then, `x xx 5x xx 1/2 xx 1/100` `= y xx 4x xx 1/2 xx 1/100` `or x/y = 4/5`. `i.e.X : Y = 4 : 5
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Question: The amount of Rs.`7500` at compound interest at `4%`per annum for `2` years is :
A
`Rs. 7800`

B
`Rs. 8100`

C
`Rs. 8112`

D
`Rs. 8082`

Note: Amount = Rs.`[ 7500 xx (1 + 4/100)^2]` `= Rs. (7500 xx 26/25 xx 26/25)` `= Rs. 8112`.
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Question: If the simple interest on a sum of money at `5%`per annum for `3` years is Rs.`1200`, the compound interest on the same sum for the same period at the same rate, is :
A
`Rs. 1260`

B
`Rs. 1261`

C
`Rs. 1264`

D
`Rs. 1265`

Note: Sum`= Rs.((100 xx 1200)/(3 xx 5))` `= Rs. 8000.` Amount`= Rs.[ 8000 xx ( 1 + 5/100)^3]` `= Rs.( 8000 xx 21/20 xx 21/20 xx 21/20)` `= Rs. 9261` :. C.I.`= Rs. (9261 - 8000)` `=Rs. 1261`.
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Question: The difference between the compound interest and the simple interest on a sum of money for `2` years at `12 1/2%`per annum is Rs.`150`.The sum is :
A
`Rs. 9000`

B
`Rs. 9200`

C
`Rs. 9500`

D
`Rs. 9600`

Note: Let the sum be Rs.x. Then, `C.I = x (1 + 25/(2 xx 100))^2 - x` `= (9/8 xx 9/8) x - x` `= (17x)/64`. `S.I = (x xx 25/2 xx 2 xx 1/100)` `= x/4` `(C.I.) - (S.I.) = ((17x)/64 - x/4)` `= x/64` `:. x/64 = 150` `or x = 9600`.
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Question: A man invests a certain sum of money at `6%` p.a.simple interest and another sum at `7%`p.a. simple interest.His income from interest after `2` years was Rs.`354`. One fourth of the first sum is equal to one fifth of the second sum. The total sum invested was :

Question: what should be the least number of years in which the simple interest on Rs. `2600` at `6 2/3%` will be an exact number of rupees ?

Question: A man invested `1/3` of his capital at `75 ; 1/4` at `8%` and the remainder at `10%`. If his annual income is Rs.`561`, the capital.

Question: A man invests an amount of Rs. `15860` in the name of his three sons A,B and C in such a way that they get the same amount after `2,3` and `4` years respectively. If the rate of simple interest is `5%` then the ratio of amounts invested among A,B and C will be :

Question: A man lends Rs. `10000` in four parts. If he gets `8%` on Rs. `2000 ; 7 1/2%` on Rs. `4000` and `8 1/2%`on Rs. `1400 ;` what percent must he get for the remainder, If his average annual interest is `8 : 13% ?`

Question: Rs.`2189` are divided into three parts such that their amounts after `1,2` and `3` years respectively may be equal, the rate of simple interest being `4%` p.a. in all case. The smallest part is ;

Question: The rates of interest in two banks A and B are inthe ratio `5 : 4. A person wants to deposit his total savings in two in such a way that he received equal fafl yearly interest from both. He should deposit the savings in banks A and B in the ratio :

Question: The amount of Rs.`7500` at compound interest at `4%`per annum for `2` years is :

Question: If the simple interest on a sum of money at `5%`per annum for `3` years is Rs.`1200`, the compound interest on the same sum for the same period at the same rate, is :

Question: The difference between the compound interest and the simple interest on a sum of money for `2` years at `12 1/2%`per annum is Rs.`150`.The sum is :