General Mathematics

Question: The radius of a wife is decreased to one third and its volume remains the same. The new length is how many times the original length ?
A
`1 times`

B
`3 times`

C
`6 times`

D
`9 times`

Note: Let, original radius = r and original length = h. New radius`= (r/3)` and let new length = H. Then, `π r^2 h = π (r/3)^2 xx H or H = 9h.`
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Question: Two cylindrical vessels with radii `15`cm and `10` cm and heights `35` cm ans `15` cm respectively are fiiled with water. If this water is poured into a cylindrical vessel `15` cm in height, then the radius of the vessel is :
A
`17.5 cm`

B
`18 cm`

C
`20 cm`

D
`25 cm`

Note: Volume of new vessel `= [π xx (15)^2 xx 35 + π xx (10)^2 xx 15]` `= 9375 π` `:. πR^2 xx 15` `= 9375π or R^2 = 625.` `So, R = 25 cm.`
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Question: A hollow garden roller `63` cm wide with a girth of `440` cm is made of iron `4` cm thick. The volume of the iron used is :
A
`57636 cm^3`

B
`54982 cm^3`

C
`56372 cm^3`

D
`58752 cm^3`

Note: Circumference of the girth` = 440 cm.` `:. 2πR = 440 ⇒ R` `= (440 xx 1/2xx 7/22)` `= 70 cm.` :. Outer radius` = 70 cm.` Inner radius `= (70 - 4) cm = 66 cm.` Volume of iron `= π [(70)^2 - (66)^2] xx 63` `= (22/7 xx 136 xx 4 xx 63) cm^3` `= 58752 cm^3.`
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Question: If `1` cubic cm of cast iron weighs `21 gms, then the weight of a cast iron pipe of lenght `1` metre `1` metre with a bore of `3` cm and in which the thickness of the metal is `1` cm, is :
A
`1.6 kg`

B
`21 kg`

C
`24.2 kg`

D
`26.4 kg`

Note: Inner radius`= 1.5,` outer radius`= 2.5 cm.` :. Volume of iron `= [π xx (2.5)^2 xx 100 - π xx (1.5)^2 xx 100] cm^3` `= 22/7 xx 100 xx [(2.5)^2 - (1/5)^2] cm^3` `= (8800/7) cm^3` :. Weight of iron `= (8800/7 xx 21/1000) kg` `= 26.4 kg.`
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Question: `60`kg of an alloy `A` is mixed with `100` kg of alloy `B`. If alloy `A` has lead and tin in the ratio `3 : 2` and alloy `B` has tin and copper in the ratio `1 : 4`, then the amount of tin in the new alloy is :
A
`36`kg

B
`44`kg

C
`53`kg

D
`80`kg

Note: Tin in `60`kg. of `A = ( 60 xx 2/5)` `= 24` kg. Tin in `100`kg of `B = ( 100 xx 1/5)` `= 20` kg. `:.`Amount of tin in new alloy `= ( 24 + 20 )` kg `= 44` kg.
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Question: `94` is divided into two parts in such a way that fifty part of first and the eighth part of the second and in the ratio `3 : 4`. The first part is :
A
`27`

B
`30`

C
`36`

D
`48`

Note: `(A / 5)/(B / 8) = 3/4` `iff A/5 xx 8/B = 3/4` `iff A/B = 3/4 xx 5/8` `= (15)/(32)`. Thus, `A : B = 15 : 32`. `:.` First part `= (94 xx (15)/(47))` `= 30`.
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Question: `33 1/3%`of a man's output is equal to `50%` of a second man's daily output. It the second man turns out `1500` screws daily, then the first man's output in terms of making screws is:
A
`500`

B
`1000`

C
`2000`

D
`2250`

Note: `(100)/(3 xx 100) A = (50)/(100) B` `iff 1/3 A = 1/2 B`. `B = 1500`. So, `1/3 A = 1/2 xx 1500 = 750`. `:. A = (3 xx 750)` `= 2250`
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Question: The sum of three numbers is `98`. If the ratio of the first to the second is `2 : 3` and that of second to the third is `5 : 8`, then the second number is :
A
`20`

B
`30`

C
`48`

D
`58`

Note: Let the numbers be `A, B` and `C`. Then, `A : B = 2 : 3` and `B : C = 5 : 8` `= 3/5 xx 5 : 3/5 xx 8` `= 3 : (24)/5`. `:. A : B : C = 2 : 3 : (24)/5` `= 10 : 15 : 24`. Second number `= (98 xx (15)/(49))` `= 30`.
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Question: If three numbers in the ratio `3 : 2 : 5` be such that the sum of their squares is `1862`, the middle number will be :
A
`7`

B
`14`

C
`21`

D
`35`

Note: Let the numbers be `3x, 2x` and `5x`. Then, `9x^2 + 4x^2 25x^2 = 1862` `iff 38x^2 = 1862` `iff x^2 = 49` `iff x = 7`. `:.`Second number `= 2x` `= 14`.
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Question: Some money is divided among three persons `A, B, C` in such a way that `5` time `A's`share, `3` times `B's` share and `2` times `C's` share are all equal. The ratio between `A, B` and `C's` shares is :
A
`5 : 3 : 2`

B
`2 : 2 : 5`

C
`15 : 10 : 6`

D
`6 : 10 : 15`

Note: `5A = 3B = 2C = k`. Then, `A = k/5, B = k/3 & C = k/2`. `:. A : B : C = k/5 : k/3 : k/2` `= 1/5 : 1/3 : 1/2` `= 6 : 10 : 15`.
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Question: The radius of a wife is decreased to one third and its volume remains the same. The new length is how many times the original length ?

Question: Two cylindrical vessels with radii `15`cm and `10` cm and heights `35` cm ans `15` cm respectively are fiiled with water. If this water is poured into a cylindrical vessel `15` cm in height, then the radius of the vessel is :

Question: A hollow garden roller `63` cm wide with a girth of `440` cm is made of iron `4` cm thick. The volume of the iron used is :

Question: If `1` cubic cm of cast iron weighs `21 gms, then the weight of a cast iron pipe of lenght `1` metre `1` metre with a bore of `3` cm and in which the thickness of the metal is `1` cm, is :

Question: `60`kg of an alloy `A` is mixed with `100` kg of alloy `B`. If alloy `A` has lead and tin in the ratio `3 : 2` and alloy `B` has tin and copper in the ratio `1 : 4`, then the amount of tin in the new alloy is :

Question: `94` is divided into two parts in such a way that fifty part of first and the eighth part of the second and in the ratio `3 : 4`. The first part is :

Question: `33 1/3%`of a man's output is equal to `50%` of a second man's daily output. It the second man turns out `1500` screws daily, then the first man's output in terms of making screws is:

Question: The sum of three numbers is `98`. If the ratio of the first to the second is `2 : 3` and that of second to the third is `5 : 8`, then the second number is :

Question: If three numbers in the ratio `3 : 2 : 5` be such that the sum of their squares is `1862`, the middle number will be :

Question: Some money is divided among three persons `A, B, C` in such a way that `5` time `A's`share, `3` times `B's` share and `2` times `C's` share are all equal. The ratio between `A, B` and `C's` shares is :