General Mathematics

Question: `A` sum of Rs. `427` is to be divided among `A, B` and `C` such that `3` times `A's` share, `4` times `B's share and `7`times `C's` share are all equal. The share of `C` is :
A
`Rs. 84`

B
`Rs. 147`

C
`Rs. 196`

D
`Rs. 240`

Note: `3A = 4B = 3C = k`. Then, `A = k/3, B = k/4` and `C = k/7`. `:. A : B : C = k/3 : k/4 : k/7` `= 28 : 21 : 12`. `:. C's` share `= Rs. (427 xx (12)/(61))` `= Rs. 84`.
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Question: If `Rs. 1540` be divided amongst `A, B, C` in such a way that the share of `B` is equal to `3/(11)` of what `A` and `C` together receive. Then, `B's` share will be :
A
`Rs. 330`

B
`Rs. 420`

C
`Rs. 880`

D
`Rs. 1210`

Note: `B = 3/(11)(A + B)`. So, `B : (A + C) = 3 : 11`. `:. B's`share `= Rs. (1540 xx 3/(14))` `= Rs. 330`.
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Question: `Rs.1870`are divided into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal. The third part is :
A
`Rs. 510`

B
`Rs. 680`

C
`Rs. 850`

D
`Rs. 1020`

Note: `A/2 = B/3 = C/6 = k`. Then `A = 2k, B = 3k` and `C= 6k`. `:. A : B : C = 2k : 3k : 6k` `= 2 : 3 : 6`. `:.` Third part `= Rs. (1870 xx 6/(11))` `= Rs. 1020`.
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Question: `Rs. 2040` are divided among `A, B, C` such that `A` gets `1/3` of what `B` gets and `B` gets `1/4` of what `C` gets. Then `B's` share is :
A
`Rs. 180`

B
`Rs. 240`

C
`Rs. 360`

D
`Rs. 480`

Note: Suppose `C` gets `Re 1`. Then, `B` gets `Re 1/4`. `A` gets `= 2/3` of `Re = 1/4 = Re 1/6`. `:. A : B : C = 1/6 : 1/4 : 1` `= 2 : 3 : 12`. `:. B's` share `= Rs. (2040 xx 3/(17))` `= Rs. 360`.
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Question: If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one ?
A
`1 : 4`

B
`1 : 8`

C
`1 : 2`

D
`8 : 1`

Note: Let original radius = R. Then, new radius` = (R/2).` `(Volume of reduced cylinder)/(Volume of original cylinder)` `=( π xx (R/2) xx h)/(π xx R^2 xx h)` `= 1/4.`
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Question: In what ratio are the volumes of a cylinder, a come and a sphere, if each has the same diameter and the same height ?
A
`1 : 3 : 2`

B
`2 : 3 : 1`

C
`3 : 1 : 2`

D
`3 : 2 : 1`

Note: Let radius = R and height = H. Then, Ratio of their volumes `= πR^2 H : 1/3 πR^2 H : 4/3 π R^3` `= H : 1/3 H : 4/3 R [In sphere H = 2R or R = H/2]` `= H :1/3 H : 4/3 xx H/2 = 3 : 1 : 2.`
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Question: The radius of a sphere is R and the radius of the base as well as the height of a cylinder is R. The ratio of the volume of the sphere to that of the cylinder is :
A
`4 : 3`

B
`3 : 4`

C
`2 : 3`

D
`3 : 2`

Note: `(Volume of sphere)/(Volume of cylinder)` `= (4/3 π R^3)/(πR^2 xx R)` `= 4/3`
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Question: Two cylinder jars have their diameters in the ratio of `3 : 1` and their heights in the ratio of `1 : 3.` The volumes are in the ratio of :
A
`1 : 2`

B
`3 : 1`

C
`3 : 4`

D
`2 : 3`

Note: Let their radio be `3x` x & heights be y & `3y`. Ratio of their volumes `= (π xx (3x)^2 xx y)/(π xx x^2 xx 3y)` `= 3/1, i e. 3 : 1.`
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Question: The volume of a sphere is `4851` cu.cm. Its curved surface area is :
A
`1716 cm^2`

B
`1386 cm^2`

C
`1625 cm^2`

D
`3087 cm^2`

Note: `4/3 xx 22/7 xx R^3` `= 4851 ⇒ R^3` `= (4851 xx 3/4 xx 7/22)` `= (21/2)^3.` `So, R = 21/2.` :. curved Surface Area `= (4 xx 22/7 xx 21/2 xx 21/2) cm^2` `= 1386 cm^2.`
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Question: The curved surface area of a sphere is `5544 sq. cm.` Its volume is :
A
`38808 cm^3`

B
`42304 cm^3`

C
`22176 cm^3`

D
`33951 cm^3`

Note: `4π R^2 = 5544 ⇒ R^2` `= (5544 xx 1/4 xx 1/22)` `= 441.` `:. R = 21.` So, volume `= (4/3 xx 22/7 xx 21 xx 21 xx 21) cm^3` `= 38808 cm^3.
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Question: `A` sum of Rs. `427` is to be divided among `A, B` and `C` such that `3` times `A's` share, `4` times `B's share and `7`times `C's` share are all equal. The share of `C` is :

Question: If `Rs. 1540` be divided amongst `A, B, C` in such a way that the share of `B` is equal to `3/(11)` of what `A` and `C` together receive. Then, `B's` share will be :

Question: `Rs.1870`are divided into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal. The third part is :

Question: `Rs. 2040` are divided among `A, B, C` such that `A` gets `1/3` of what `B` gets and `B` gets `1/4` of what `C` gets. Then `B's` share is :

Question: If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one ?

Question: In what ratio are the volumes of a cylinder, a come and a sphere, if each has the same diameter and the same height ?

Question: The radius of a sphere is R and the radius of the base as well as the height of a cylinder is R. The ratio of the volume of the sphere to that of the cylinder is :

Question: Two cylinder jars have their diameters in the ratio of `3 : 1` and their heights in the ratio of `1 : 3.` The volumes are in the ratio of :

Question: The volume of a sphere is `4851` cu.cm. Its curved surface area is :

Question: The curved surface area of a sphere is `5544 sq. cm.` Its volume is :