General Mathematics

Question: A profit of Rs. `30000` is to distributed among `A, B, C` in the proportion `3 : 5 : 7`. What will be the difference between `B's` and `C's` shares ?
A
`Rs. 2000`

B
`Rs. 4000`

C
`Rs. 10000`

D
`Rs. 14000`

Note: `B's` share `= Rs. (30000 xx 5/(15))` `= Rs. 10000`. `C's` share `= Rs. (30000 xx 7/(15))` `= Rs. 14000`. `:.` Difference in `B's & C's ` shares `= Rs. 4000`.
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Question: Rs. `407` are to be divided among `A, B` and `C` so that their shares are in the ratio of `1/4 : 1/5 : 1/6`. The respective shares of `A, B, C` are :
A
`Rs. 165, Rs. 132, Rs. 110`

B
`Rs. 165, Rs. 110, Rs. 132`

C
`Rs. 132, Rs. 110, Rs. 165`

D
`Rs. 110, Rs. 132, Rs. 165`

Note: `A : B : C = 1/4 : 1/5 : 1/6` `= 15 : 12 : 10` `A's` share `= Rs. (407 xx (15)/(37))` `= Rs. 165`, `B's` share `= Rs. (407 xx (12)/(37))` `= Rs. 132`, `C.s` share `= Rs. [407 - (165 + 132)]` `= Rs. 110`
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Question: If Rs `1066` are divided among `A, B, C` and `D` such that `A : B = 3 : 4, B : C = 5 : 6`and `C : D = 7 : 5`, who will get the maximum ?
A
`B`

B
`A`

C
`C`

D
`D`

Note: `A : B = 3 : 4`, `B : C = 5 : 6` `= 5 xx 4/5 : 6 xx 4/5` `= 4 : (24)/5`. `:. A : B : C = 4 : (24)/5` `= 15 : 20 : 24 & C : D = 7 : 5` or `A : B : C = 15 : 2o : 24 & C : D = (24)/7 xx 7 : (24)/7 xx 5` or` A : B : C = 15 : 2o : 24 & C : D = 24 : (120)/7`. `:. A : B : C : D = 15 : 20 : 24 : (120)/7` `= 105 : 140 : 168 : 120` Clearly, `C` will get the maximum amount.
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Question: A certain amount was divided between Salim and Rahim in the ratio of `4 : 3`. If Rahim's share was Rs. `2400`, the total amount was :
A
`Rs. 5600`

B
`Rs. 3200`

C
`Rs. 9600`

D
`Rs. 16800`

Note: Let `S =4x` and `R = 3x`. Total amount `= 7x` Then, `3x = 2400` `iff x = 800`. `:.` Total amount `= 7x` `= Rs. 5600`
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Question: The ratio of the ages of mother and son is `7 : 3`. If the sum of their ages is `60` years, what is the difference in their ages ?
A
`42` years

B
`24` years

C
`18` years

D
`4` years

Note: Mother's age `= (60 xx 7/(10))` `= 42` years. Son's age `=(60 - 42)`years `= 18`years. Difference of their ages `= (42 - 18)`years `= 24` years.
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Question: The speeds of the ages of three cars are in the ratio `5 : 4 : 6`. The ratio between the times taken by them to travel the same distance is :
A
`5 : 4 : 6`

B
`6 : 4 : 5`

C
`10 : 12 : 15`

D
`12 : 15 : 10`

Note: Ratio of times taken `= 1/5 : 1/4 : 1/6` `= 12 : 15 : 10`
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Question: The sides of a triangle are in the ratio `1/2 : 1/3 : 1/4` and its perimeter is `104 cm`. The length of longest side is :
A
`52 cm`

B
`48 cm`

C
`32 cm`

D
`26 cm`

Note: Ratio of sides `= 1/2 : 1/3 : 1/4` `= 6 : 4 : 3`. Largest side `= ( 104 xx 6/(13)) cm` `= 48 cm`.
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Question: In a college, the ratio of the number of boys to girls is `8 : 5`. If there are `160` girls, the total number of students in the college is :
A
`100`

B
`250`

C
`260`

D
`416`

Note: Let the number of boys and girls be `8x` and `5x`. Then , total number of students `= 13x`. Now, `5x = 160` `iff x = 32`. `:.` Total number of students `= 13x ` `= 13 xx 32` `= 416`.
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Question: The prices of a scooter and T.V. are in the ratio of `5 : 4`. If the scooter costs Rs. `4000` more than the T.V. set , the price of a T.V. set (in rupees) is :
A
`12000`

B
`14000`

C
`16000`

D
`20000`

Note: Let the costs of scooter & T.V. be `5x` and `4x`. Then, ` 5x - 4x = 4000` `iff x = 4000`. `:.` Cost of a T.V. `= 4x` `= Rs. 16000`.
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Question: The dimensions of an open box are `50` cm, `40` cm and `23 cm.` Its thickness is `3 cm.` If `1` cubic cm of metal used in the box weighs `0.5 gms,` the weight of the box is :
A
`8.56 kg`

B
`8.04 kg`

C
`7.576 kg`

D
`6.832 kg`

Note: Volume of the metal `= [(50 xx 40 xx 23) - (44 xx 34 xx 20)] cu. cm.` `= 16080 cu. cm.` Weight of the metal `= ((16080 xx 0.5)/1000) kg` `= 8.04 kg.`
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Question: A profit of Rs. `30000` is to distributed among `A, B, C` in the proportion `3 : 5 : 7`. What will be the difference between `B's` and `C's` shares ?

Question: Rs. `407` are to be divided among `A, B` and `C` so that their shares are in the ratio of `1/4 : 1/5 : 1/6`. The respective shares of `A, B, C` are :

Question: If Rs `1066` are divided among `A, B, C` and `D` such that `A : B = 3 : 4, B : C = 5 : 6`and `C : D = 7 : 5`, who will get the maximum ?

Question: A certain amount was divided between Salim and Rahim in the ratio of `4 : 3`. If Rahim's share was Rs. `2400`, the total amount was :

Question: The ratio of the ages of mother and son is `7 : 3`. If the sum of their ages is `60` years, what is the difference in their ages ?

Question: The speeds of the ages of three cars are in the ratio `5 : 4 : 6`. The ratio between the times taken by them to travel the same distance is :

Question: The sides of a triangle are in the ratio `1/2 : 1/3 : 1/4` and its perimeter is `104 cm`. The length of longest side is :

Question: In a college, the ratio of the number of boys to girls is `8 : 5`. If there are `160` girls, the total number of students in the college is :

Question: The prices of a scooter and T.V. are in the ratio of `5 : 4`. If the scooter costs Rs. `4000` more than the T.V. set , the price of a T.V. set (in rupees) is :

Question: The dimensions of an open box are `50` cm, `40` cm and `23 cm.` Its thickness is `3 cm.` If `1` cubic cm of metal used in the box weighs `0.5 gms,` the weight of the box is :