General Mathematics

Question: A man can row three quarters of a kilometre against the stream in `11 1/4` minutes and returns in `7 1/2` minutes. The speed of the man is still water is :
A
`2 km∕hr`

B
`3 km∕hr`

C
`4 km∕hr`

D
`5 km∕hr`

Note: Speed upstream `= (3/4 xx 4/45 xx 60) kmph` `= 4 kmph.` Speed downstream `= (3/4 xx 2/15 xx 60) kmph` `= 6 kmph.` Speed in still water `= 1/2 (6 + 4) kmph` `= 5 kmph`
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Question: An ornament weighs `12.5` gms of which `2.5` gm is pure silver and the rest alloy. The ratio of pure silver to alloy is :
A
`1 : 4`

B
`1 : 5`

C
`4 : 1`

D
`4 : 5`

Note: pure silver : Alloy `= 2.5 : (12.5 -2.5)` `= 2.5 : 10` `= 1 : 4`.
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Question: The marks obtained by Praveen and Vijay are in the ratio of `4 : 5`and those obtained by Vijay and Suresh are in the ratio of `3 : 2`. The marks obtained by Praveen and Suresh are in the ratio of :
A
`2 : 1`

B
`5 : 3`

C
`6 : 5`

D
`5 : 6`

Note: `P : V = 4 c: 5` and `V : S = 3 : 2` `P/V = 4/5` and `V/S = 3/2`, so, `P/S = P/V xx V/S` `= 4/5 xx 3/2` `= 6/5`.
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Question: Anshul got twice as many marks in English as in Science. His total marks in English, Science and Maths are `180`. If the proportion of his marks in English and Maths is `2 : 3`, what are his marks in Science ?
A
`15`

B
`30`

C
`60`

D
`90`

Note: `E = 2S, E + S + M = 180` `iff E + 1/2E + M = 180` `:. 3E + 2M = 360` and `E/M = 2/3` or `M = 3/2E.` `:. 3E + 2 xx 3/2E = 360` or `E = 60.` `:. S = 1/2E = 1/2 xx 60` `= 30`.
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Question: Two numbers are in the ratio `3 : 4` and the product of their L.C.M. and H.S.C. is `10800`. The sum of the numbers is :
A
`180`

B
`210`

C
`225`

D
`240`

Note: Let the numbers be `3x` and `4x`. Then, `3x xx 4x = 10800` `iff 12x^2 = 10800` `iff x^2 = 900` `iff x = 30`. `:.` Sum of numbers `= 7x` `=7 xx 30` `= 210`.
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Question: The ages of `X` and `Y` are in the ratio of `3 : 1`. Fifteen years hence, the ratio will be `2 : 1`. Their present ages (in years) are :
A
`30, 10`

B
`45, 15`

C
`21, 7`

D
`60, 20`

Note: Let the ages of `X` and `Y` be `3x` and `x`. `(3x + 15)/(X + 15) = 2/1` or `3x + 15 = 2x + 30` or `x = 15`. `:.` Present ages of `X` and `Y` are `45` years and `15` years respectively.
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Question: The ratio of the number of boys and girls in a school is `3 : 2`. It `20%` of the boys and `25%` of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is :
A
`56`

B
`70`

C
`78`

D
`80`

Note: Let boys `= 3x` & girls `= 2x`. Number of those who are not scholarship holders `= 80% of 3x + 75% of 2x` `=((80)/(100) xx 3x + (75)/(100) xx 2x)` `=(39x)/(10)`. `=(78)/(100) xx (5x)` `= 78%` of the total.
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Question: If `40%` of `40%` of x `= 40,` then x is :
A
`100`

B
`400`

C
`250`

D
`1000`

Note: `40/100 xx 40/100 xx x = 40 ⇒ x` `= (40 xx 100 xx 100)/(40 xx 40)` `= 250`
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Question: `√3.6% of 40 = ?`
A
`2.8`

B
`1.8`

C
`1.2`

D
None

Note: `√3.6% of 40` `= √(3.6)/100 xx 40` `= √144/100` `= 12/10` `= 1.2`
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Question: By how much percent is four-fifth of`70` lesser than five-seventh of`112 ?`
A
`42%`

B
`30%`

C
`24%`

D
`36%`

Note: `4/5 xx 70` `= 56 & 5/7 xx 112` `= 80` Decrease over`80 = (80 - 56)` `= 24` Decrease over`100 = (24/80 xx 100)%` `= 30%`
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Question: A man can row three quarters of a kilometre against the stream in `11 1/4` minutes and returns in `7 1/2` minutes. The speed of the man is still water is :

Question: An ornament weighs `12.5` gms of which `2.5` gm is pure silver and the rest alloy. The ratio of pure silver to alloy is :

Question: The marks obtained by Praveen and Vijay are in the ratio of `4 : 5`and those obtained by Vijay and Suresh are in the ratio of `3 : 2`. The marks obtained by Praveen and Suresh are in the ratio of :

Question: Anshul got twice as many marks in English as in Science. His total marks in English, Science and Maths are `180`. If the proportion of his marks in English and Maths is `2 : 3`, what are his marks in Science ?

Question: Two numbers are in the ratio `3 : 4` and the product of their L.C.M. and H.S.C. is `10800`. The sum of the numbers is :

Question: The ages of `X` and `Y` are in the ratio of `3 : 1`. Fifteen years hence, the ratio will be `2 : 1`. Their present ages (in years) are :

Question: The ratio of the number of boys and girls in a school is `3 : 2`. It `20%` of the boys and `25%` of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is :

Question: If `40%` of `40%` of x `= 40,` then x is :

Question: `√3.6% of 40 = ?`

Question: By how much percent is four-fifth of`70` lesser than five-seventh of`112 ?`