General Mathematics

Question: A wholesaler gains 25% by selling a commodity and a retailer gains 30% by selling it. If the retail value of that commodity is Rs. 325, then the wholesale value is :
A
Rs. 200

B
Rs. 225

C
Rs. 245

D
Rs.255

Note: Retailer,s value` = (100/130 xx 325) = 250` Wholesaler,s value` = (100/125 xx 250) = 200`
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Question: A shopkeeper decides to give 5% commission on the marked price of an article but also wants to earn 10% profit. If the cost price is Rs. 95, then the marked price is :
A
Rs. 100

B
Rs.105

C
Rs.110

D
Rs.115

Note: S.P` = ((110)/(100) xx 95)` `= ((209)/(2))` commission = 50% :. M.P.` = (110/95 xx 209/2) = 110.`
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Question: A bag contains 25-p, 10 p-and-p coins in the ratio 1 : 2 : 3. If the total value is Rs. 30, the number of 5-p coins is :
A
50

B
100

C
200

D
150

Note: Let these coins be x 2x and 3x. Then, `25/(100) x + 10/(100) xx 2x + 5/(100) xx 3x => 60 x` ` = 30 xx 100 => x = 50` Number of 5 p- coins = 3x = 150
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Question: If (x + y) : (x - y) = 4 : 1, then `(x^2 + y^2) : (x^2 - y^2) = ?`
A
25 : 9

B
16 :1

C
8 : 17

D
17 : 8

Note: `(x + y)/(x - y) = 4/1 => x + y` `= 4x - 4y => 3x = 5y => x/y = 5/3.` `:. (x^2 + y^2)/(x^2 - y^2)` `= (x^2/(y^2) + 1)/(x^2/(y^2) - 1)` `= ((x/y)^2 + 1)/((x/y)^2 - 1)` `= 34/16 = 17/8`
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Question: `9^(3.04) : 9^(2.04) = ?`
A
1 : 9

B
3 : 2

C
76 : 51

D
None of these

Note: `(9^(3.04))/(9^(2.04))` ` = 9^(3.04 - 2.04)` `= 9^1 = 9/1.`
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Question: If a : b = b : c, then` a^4 : b^4 = ?`
A
`ac = b^2`

B
`a^2 : c^2`

C
`c^2 : a^2`

D
`b^2 : ac`

Note: Let` a/b = b/c =k.` Then, `b = ck and a = bk = ck^2` `:. a^4/b^4 = (c^4 k^8)/(c^4 k^4)` `= k^4 and a^2/c^2 = (c^2 k^4)/c^2 = k^4` Hence,` a^4/b^4` `= a^2/c^2`
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Question: If` x : y = 3 : 4,` then `(2x + 3y) : (3y - 2x) = ?`
A
`2 : 1`

B
`3 : 2`

C
`3 : 1`

D
`21 : 1`

Note: Given `x/y = 3/4` `:. (2x + 3y)/(3y - 2x)` `= (2 (x/y) + 3)/(3 - 2 (x/y)` `= (2 xx (3/4) + 3)/(3 - 2 xx (3/4)` `= 18/6 = 3/1`
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Question: The sum of three numbers is 174. The ratio of second number to the third number is 9 : 16 and the ratio of first number to the third one is 1 : 4. The second number is :
A
24

B
54

C
96

D
can not be determind

Note: A` = 1/2 (B + c) => B + C = 2A => A + B + c = 3A` B` = 1/2 ( A + C) => 4B = A + C => A + B + C = 5B` `:. 3A = 56250 and 5B = 56250 => A = 18750 and B = 11250` `:. A - B = (18750 - 11250) = 7500.`
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Question: 5 mangoes and oranges cost as much as 3 mangoes and 7 oranges. What is the ratio of the cost of one mango to that of one orange ?
A
`4 : 3`

B
`1 : 3`

C
`3 : 2`

D
`5 : 2`

Note: Let cost of each mango be x paise and that of each orange be y paise then `5x + 4y = 3x + 7y => 2x` ` = 3y => x : y = 3 : 2`
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Question: If 35% of A,s income is equal to 25% of B,s income, then the ratio of their incomes is :
A
`4 : 3`

B
`5 : 7`

C
`7 : 5`

D
`4 : 7`

Note: `35/(100) x = 25/(100) y => x/y` `= (25)/(35) = 5/7 => x : y = 5 : 7`
1. Report

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Question: A wholesaler gains 25% by selling a commodity and a retailer gains 30% by selling it. If the retail value of that commodity is Rs. 325, then the wholesale value is :

Question: A shopkeeper decides to give 5% commission on the marked price of an article but also wants to earn 10% profit. If the cost price is Rs. 95, then the marked price is :

Question: A bag contains 25-p, 10 p-and-p coins in the ratio 1 : 2 : 3. If the total value is Rs. 30, the number of 5-p coins is :

Question: If (x + y) : (x - y) = 4 : 1, then `(x^2 + y^2) : (x^2 - y^2) = ?`

Question: `9^(3.04) : 9^(2.04) = ?`

Question: If a : b = b : c, then` a^4 : b^4 = ?`

Question: If` x : y = 3 : 4,` then `(2x + 3y) : (3y - 2x) = ?`

Question: The sum of three numbers is 174. The ratio of second number to the third number is 9 : 16 and the ratio of first number to the third one is 1 : 4. The second number is :

Question: 5 mangoes and oranges cost as much as 3 mangoes and 7 oranges. What is the ratio of the cost of one mango to that of one orange ?

Question: If 35% of A,s income is equal to 25% of B,s income, then the ratio of their incomes is :