General Mathematics

Question: What is the ratio whose terms differ by `40` and the measure of which is `2/7` ?
A
`16 : 56`

B
`10 : 50`

C
`20 : 70`

D
`36 : 76`

Note: `x/(x + 40) = 2/7` `iff 7x = 2x + 80` `iff x = 16`. `:.`The ratio is `16 : 56`.
1. Report
Question: If `x^2 + 4y^2 = 4xy`, then `x : y` is :
A
`2 : 1`

B
`1 : 2`

C
`1 : 1`

D
`1 : 4`

Note: `x^2 + 4y^2 = 4xy` `iff x^2 - 4xy + 4y^2 = 0` `iff (x - 2y)^2 = 0` `iff x -2y = 0` `iff x = 2y` `iff x/y = 2/1`.
1. Report
Question: If `5x^2 - 13xy + 6y^2 = 0`, then `x : y` is :
A
`5 : 3` or `1 : 2`

B
`3 : 5` or `2 : 1`

C
`2 : 1` only

D
`3 : 5` only

Note: `5x^2 - 13xy + 6y^2 = 0` `iff 5x^2 - 10xy - 3xy + 6y^2 = 0` `iff 5x (x - 2y) - 3y (x - 2y) = 0` `iff (x - 2y)(5x - 3y) = 0` `iff x - 2y = 0` or `5x - 3y = 0` `iff x = 2y` or `5x = 3y` `iff x : y = 2 : 1` or `x : y = 3 : 5`.
1. Report
Question: A sum of money at compound amount which earns Rs. `578.40` in `2` years and to Rs.`614.55` in `3` years.The rate of interest per annum is :
A
`4%`

B
`5%`

C
`6 1/4%`

D
`8 1/3%`

Note: Interest on Rs.`578.40` for `1` year` = Rs.(614 - 578.40)` `=Rs. 36.15` :. Rate` = ((100 xx 36.15)/578.40)%` `= 6 1/4%`.
1. Report
Question: what is the principal amount which earns Rs.`132` as compound interest for the second year at `10%` per annum ?
A
`Rs.1000`

B
`Rs. 1200`

C
`Rs. 1320`

D
`Rs. 1188`

Note: Let the principal at the end of first year be Rs.x. Then,`(x xx 10 xx 1)/100` `= 132` `or x = 1320`. Now,let the original principal be Rs.p Then, amount after `1` year `= p + (p xx 10 xx 1)/100` `= (11p)/10`. `:. (11p)/10 = 1320` `or p = (1320 xx 10)/11` `= Rs. 1200`.
1. Report
Question: A sum of money at compound interest amounts to Rs.`5290` in `2` years and to Rs.`6083.50` in `3` years. The rate of interest per annum is :
A
`12%`

B
`14%`

C
`15%`

D
`16 2/3%`

Note: Interest on Rs.`5290` for `1` years `= Rs. (6083.50 - 5290)` `= Rs.793.50` `:. Rate = ((100 xx 793.50)/5290)%` `= 15%`.
1. Report
Question: If the amount is `2 1/4` times the sum after `2` years at compound interest ,the rate of interest per annum is :
A
`25%`

B
`30%`

C
`40%`

D
`50%`

Note: `p(1 + R/100)^2` `= 9/(4) p ⇔ (1 + R/100)^2` `= 9/4 = (3/2)^2`. `:. 1 + R/100 = 3/2` `or R/100 = 1/2` `or R = 50`.
1. Report
Question: A sum of money amounts to Rs.`4624` in`2` years and to Rs.`4913` in `3` years at compound interest. The sum is :
A
`Rs. 4096`

B
`Rs. 4260`

C
`Rs. 4335`

D
`Rs. 4360`

Note: Interest on Rs.`4624` for `1` year `= Rs. (6083.50 - 5290)` `= Rs.793.50` :.Rate `= ((100 xx 793.50)/(4624 xx 1)%` `= 6 1/4%`. Now, x `(1 + 25/(4 xx 100))^2 = 4624` `or x xx 17/16 xx 17/16 = 4624` `:.x = (46 xx 16/17 xx 16/17)` `= Rs. 4096`.
1. Report
Question: A sum of money placed at compound interest doudles itself in `5` years. It will amount to eight times itself in :
A
`10 years`

B
`12 years`

C
`15 years`

D
`20 years`

Note: `p (1 + R/100)^5` `= 2p ⇒ (1 + R/100)^5 = 2` Let `p (1 + R/100)^n` `= 8p.` Then, `(1 + R/100)^n = 8 = 2^3` `= {(1 + R/100)^5}^3` `= (1 + R/100)^15` `:. n = 15 years`.
1. Report
Question: A sum of money at compound interest amounts to thrice itself in `3` years. In how many years will it be `9` times itself ?
A
`12`

B
`9`

C
`6`

D
`8`

Note: `p (1 + R/100)^3` `= 3p ⇒ (1 + R/100)^3 = 3` Let` p(1 + R/100)^n` `= 9p ⇒ (1 + R/100)^n = 9` `:. (1 + R/100)^n = 3^2` `= [(1 + R/100)^3]^2` `= (1 + R/100)^6` Hence,n` = 6 `years.
1. Report

First Prev 60 61 62 63 64 Next Last

Question: What is the ratio whose terms differ by `40` and the measure of which is `2/7` ?

Question: If `x^2 + 4y^2 = 4xy`, then `x : y` is :

Question: If `5x^2 - 13xy + 6y^2 = 0`, then `x : y` is :

Question: A sum of money at compound amount which earns Rs. `578.40` in `2` years and to Rs.`614.55` in `3` years.The rate of interest per annum is :

Question: what is the principal amount which earns Rs.`132` as compound interest for the second year at `10%` per annum ?

Question: A sum of money at compound interest amounts to Rs.`5290` in `2` years and to Rs.`6083.50` in `3` years. The rate of interest per annum is :

Question: If the amount is `2 1/4` times the sum after `2` years at compound interest ,the rate of interest per annum is :

Question: A sum of money amounts to Rs.`4624` in`2` years and to Rs.`4913` in `3` years at compound interest. The sum is :

Question: A sum of money placed at compound interest doudles itself in `5` years. It will amount to eight times itself in :

Question: A sum of money at compound interest amounts to thrice itself in `3` years. In how many years will it be `9` times itself ?