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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
` 2/3 : 4/9` is equal to _________A. 18:12B. `6:4`C. ` 3:2`D. All of these |
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Answer» Correct Answer - D ` 2/3 : 4/9` ` = 2/3 xx 9 : 4/9 xx 9 = 18 : 12` ` = 6 : 4 = 3 :2 ` Hence, the correct option is (d). |
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| 52. |
Cost of 5 kg of wheat is Rs 30.50.(a) What will be the cost of 8 kg of wheat?(b) What quantity of wheat can be purchased in Rs 61? |
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Answer» a)5kg wheat=30.5Rs 1kg wheat=30.5/5Rs=6.1Rs 8kg wheat=8*6.1=48.8Rs. b)6.1Rs=1kg Wheat 1Rs=1/6.1kg Wheat 61Rs=61/6.1=10Kg wheat. |
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| 53. |
The weight of 72 books is 9 kg. What is the weight of 40 such books? |
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Answer» Weight of 72 books `= 9kg` Weight of one book ` = 9/72kg` Weight of 40 such books ` = 9/72**40 = 5kg` |
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| 54. |
if `x : 5 : : 4 : 20, then x = _________ |
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Answer» Correct Answer - 1 x : 5 : : 4: 20 ` Rightarrow x/5 = 4/20` ` x/5 = 1/5` x =1 |
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| 55. |
if 3, x, 6, 12 ar in proportion , then x = |
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Answer» Correct Answer - 6 3x,6, 12 are in proportion. ` 3/x = 6/12 Rightarrow 3/x = 3/6` x = 6 |
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| 56. |
A car travels 90 km in `(2)1/2` hours. (a) How much time is required to cover 30 km with the same speed? (b) Find the distance covered in 2 hours with the same speed. |
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Answer» a)90km=2.5hrs 1km=2.5/90hrs=1/36hrs 30km=30/36=.83hrs=50min b)2.5hrs=90km 1hr=90/2.5km=36km 1hrs=2*36=72km. |
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| 57. |
if p,q,r and s are in proportion then `p/q` = _________ |
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Answer» Correct Answer - ` r/s` p,q, r ,s are in proportion P: q :: r:s `p/q = r/s` |
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| 58. |
The ratio of 10 m to 1 km is ____A. `10:1`B. `1 : 10`C. `1 : 100`D. `100 : 100` |
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Answer» Correct Answer - C 10 m : 1 km = 10 m : 1000 m ` 10 xx 1 : 10 xx 100 =1 : 100` Hecne, the correct option is ( c) . |
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| 59. |
`{:("Column A"," Column B"),((a)1/3:2/5,(p) 20:3),((b) 3/4:5/2, (q)3:10),((c)2/3:3/5,(r)5:6),((d)4/3:1/5,(s)10:9):}` |
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Answer» Correct Answer - A::B::C::D ` (a) 1/2 : 2/5 = 5:6 to (r )` `(b) 3/4 : 5/2 = 3 : 10 to (q)` ` ( c) 2/3 : 3/5 = 10 : 9 to (s)` ` (d) 4/3 : 1/5 = 20 : 3 to (p) ` |
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| 60. |
If 1,2,3 x are in proprotions then x= ___________ |
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Answer» Correct Answer - 6 1,2,3, x are in proportion. 1 (x) = 2(3) x = 6 |
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| 61. |
At a given point of time, the heights of trees are in proportion to the lengths of the shadows of the trees. A tree of height 25.6 m casts a shadow of 32 m. if the shadow of another tree at that point of time is 48m, then find the height of that tree. |
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Answer» Correct Answer - 38.4 m Given 32 : 48 : : 25.6 :x ` 32 / 48 = ( 25.6)/x Rightarrow 2/3 = (25.6)/x` x `= 25.6 xx 3/2 = 38.4 m` |
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| 62. |
Are 30, 40, 45 and 60 in proportion? |
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Answer» 30/40=3:4 40/45=3:4 45/60=3:4 So, we can say that they are in proportion. |
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| 63. |
Check whether the following are in proportion or not : (i) 2,4,6,8 (ii) 12, 18, 10 ,15 |
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Answer» (i) product of extremes = `2 xx 8 = 16` Product of means = `4xx 6 = 24` ` 16 ne 24` 2,4,6,8 are not in prodortion. (ii) Porduct of means = ` 18 xx 10 = 180 ` Porduct of exterms = product of means Product of exterms = `12 xx 15 =180` 12,18, 10, 15 are in proportions. |
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| 64. |
250 mL of water is added to 750 mL of milk. Find the ratio of milk and water in the solution. |
| Answer» 750 mL = 750 : 250 = 75 : 25 = 3:1 | |
| 65. |
Divide the amount ₹ 540 in the ratio 5 :4 |
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Answer» The sum of the terms of the ratio 5 + 4=9 The required amounts are `5/9 ( ₹ 540) and 4/9 ( ₹ 540) ` , i.e. ₹ 300 and ₹ 240 |
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| 66. |
The simplest form of 8 :12 is _______ |
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Answer» Correct Answer - `2:3` ` 8 : 12 = 4 xx 2 :4 xx 3 = 2 :3` |
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| 67. |
Write the following in their simplest forms. (i) 32 : 80 (ii) `8/15 : 7/12` |
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Answer» (i) 32:80=2:5 (ii)` 8/15 : 7/12` The LCM of 15 and 12 is 60. ` 8/16 xx 60 : 7/12 xx 60 = 32: 35` |
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| 68. |
Find the ratio of the following and express them in the simplest form (i) 360 mL , 500 mL (ii) 4 h 20 min , 6 h |
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Answer» Correct Answer - (i) 18 : 25 (ii) 13 : 18 (i) 360 mL, 500 mL 360 : 500 = 36 : 50 (ii) 4 h 20 min : 6 h `= ( 4 xx 60 + 20) : 6 xx 60 = 360 : 360 ` 26 : 36 = 13 : 18 |
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| 69. |
`{:("column A" , "column B"),((a) x:5 : : 2:3, (p)6/5),((b)2:x: : 4 :3, (q) 15/2),((c) 2:5 : :x:3,(r) 10/3),((d)2:5 ::3:x , (s)3/2):}` |
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Answer» Correct Answer - A::B::C::D x : 5 : : 2 : 3 ` x/5 = 2/3` ` Rightarrow x= 10/3 to ( r) ` (b) 2 : x : : 4 : 3 ` Rightarrow 2/x = 4/3 ` ` Rightarrow x = 2 xx 3/4 = 6/4 = 3/2 to (s)` ( c) 2 :5 : : 3 : x `2/5 = 3/x` ` Rightarrow x = 3 xx 5/2` ` x = 15/2 to (q)` Therefore, the correct mathch is : ` a to r, b to s, c to p, d to q ` |
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| 70. |
The length and the breadth of a rectangle are in the ratio 12: 5. if the length of the rectangle is 48 cm , then the breadth of the rectangle is _____A. 20 cmB. 30 cmC. 40 cmD. 50 cm |
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Answer» Correct Answer - A 12 : 5 = 48 : x ` 12/5 = 48/x` ` x = 48/12 xx 5` `x = 4xx 5` x = 20 cm Hence, the correct option is (a) |
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| 71. |
The ratio between the quantities `1.5` kg and 80 gms is -A. `4 : 75`B. `75 : 4`C. `2 : 25`D. `4 : 25` |
| Answer» Correct Answer - B | |
| 72. |
The ratio between the quantities 15 dcm and 15 mm is -A. `100 : 1`B. `1 : 1`C. ` 1 : 100`D. ` 2 : 25` |
| Answer» Correct Answer - A | |
| 73. |
Four quantities a,b,c d are siad to be proportion if ______ |
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Answer» Correct Answer - ad = bc ad = bc |
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| 74. |
What number should be added to each term of the ratio `2a : 3b ` so that the ratio of the additions will be `c : d`? |
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Answer» Let the number x should be added to each term. As per question, `(2a + x) : (3b + x) = c : d` or, `(2a + x)/(3b + x) = c/d " or, 2ad " + dx = 3bc + cx` or, ` dx - cx = 3bc -2ad` or, ` x (d -c) = 3bc - 2ad` or, ` x = (-(2ad - 3bc))/(d-c) " or , " x = (-(2ad - 3bc))/(-(c-d))` or, ` x = (2ad - 3bc)/(c -d)` Hence the required number ` = (2ad - 3bc)/(c-d)` |
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| 75. |
If `p : q = 5 : 7 " and " p - q = - 4`, then find the value of ` (3p + 4q)`. |
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Answer» We have , ` p : q = 5 : 7 " or, " p/q = 5/7 = (5k)/(7k) [k ne 0]` ` :. ` Let ` [ = 5k " and " q = 7k`. Also, ` p - q = - 4 " or, " 5k - 7k = - 4 " or, " - 2k = - 4 " or, " k = (-4)/(-2) = 2`. ` :. P = 5k = 5 xx 2 = 10 " and " q = 7k = 7 xx 2 = 14`. ` :. 3p + 4q = 3 xx 10 + 4 xx 14 = 30 + 56 = 86`. Hence the required value = 86. |
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| 76. |
If ` a : b = 3 : 4 " and " x : y = 4 : 5`, then find the value of `(3ax - by)/(5by-7ax)` |
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Answer» Given that , ` a : b = 3 : 4, :. a/b = 3/4` Again, ` x : y = 4 : 5 " or, " x/y = 4/5` Now, Given quantity ` = (3ax-by)/(5by - 7ax) = ((3ax)/(by) - 1)/(5-(7ax)/(by)) ` [Dividing by ] ` = (3. 1/b*x/y-1)/(5 - 7 . a/b * x/y)` ` = (3xx 3/4 xx 4/5 -1)/(5 - 7 xx 3/4 xx 4/5)` ` = (9/5 -1)/(5-21/5) = ((9-5)/5)/((25-21)/5) = (4/5)/(4/5) = 1` Hence the required value = 1. |
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| 77. |
If `(5x - 3y) : (2x + 4y) = 11 : 12`, then find ` x : y`. |
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Answer» Given that, ` (5x- 3y) : (2x + 4y) = 11 : 12` or, `(5x - 3y)/(2x + 4y) = 11/12` or, ` 60x - 36y = 22x + 44y` or, ` 60x - 22x = 44y + 36y` or, ` 38x = 80y` or, ` x/y = 80/38 " or, " x/y = 40/19` ` :. X : y = 40 : 19`. |
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| 78. |
What term should be subtracted each of the ratio `a : b` to make the ratio `m : n` ? |
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Answer» Let x should be subtracted from each term. As per question, `(a - x) : (b -x) = m : n` or, `(a-x)/(b-x) = m/n` or, `mb - mx = na - nx` or, `nx - mx = na - mb` or, `x ( n -m) = na - mb` or, ` x = (na - mb)/(n -m) = (bm - an)/(m-n)` Hence `(bm -an)/(m-n) ` should be subtracted. |
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| 79. |
If `(10 x + 3y) : (5x + 2y) = 9 : 5`, then show that `(2x + y) : (x + 2y) = 11 : 13`. |
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Answer» `(10 x + 3y) : (5x + 2y) = 9 : 5` or , `(10x + 3y)/(5x + 2y) = 9/5` or, `50x + 15y = 45x + 18y` or, `50x - 45x = 18y -15y` or, `5x = 3y " or, " x/y = 3/5` or, `x/y = (3k)/(5k) [k ne 0]` ` :. ` let x = 3k and y = 5k. Now, ` (2x + y) : (x + 2y) = (2x + y)/(x + 2y)` ` = (2 xx 3k + 5k)/(3k + 2 xx 5k)` ` = (6k + 5k)/(3k+10k) = (11k)/(13k) = 11/13`. Hence `(2x + y) : (x +2y) = 11 : 13`. |
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| 80. |
Goldis 19 times a heavy as water andcopper is 9 times as heavy is water. In what ratio should these be mixed toget an alloy 15 times as heavy is waster?`1:1`b. `1:2`c. `2:3`d. `3:2` |
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Answer» Let the weight of water be Wtherefore, weight of gold `=19W` and weight of copper `=9W` therefore weight of alloy `=15W` Ratio of G:C = 1:y Therefore total = 1+y `19W+y(9W)= (1+y)15W` `19W+9yW = 15W+15Wy` `4W = 6Wy` `y = (6W)/(4W)` `y = 3:2` which is the required ratio. |
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| 81. |
If ` x^(2) : (by + cz) =y^(2) : (cz + ax) = z^(2) : (ax + by) = 1`, then show that ` a/(a+x) + b/(b+y) + c/(c+z) = 1`. |
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Answer» `x^(2) : (by + cz) = y^(2) : (cz+ax) = z^(2) : (ax + by) = 1`. or, ` x^(2)/(by + cz) = y^(2)/(cz + ax) = z^(2)/(ax + by) = 1`. ` :. X^(2)/(by+cz) = 1 rArr x/(by+cz) = 1/x` [Dividing by x ] ` rArr (ax)/(by + cz) = a/x ` [Multiplying by a] `rArr (ax)/(ax + by + cz) = a/(a + x) ` [by componendo process] ` :. (ax)/(ax + by + cz) = a/(a + x) ` ...............(1) Similarly , it can be proved that ` (by)/(ax + by + cz) = b/(b +y) ` ....................(2) and `(cz)/(ax + by + cz) = c/(c+z) ` ..................(3) Now , adding (1), (2) and (3) we get, ` (ax)/(ax + by+cz) + (by)/(ax+by+cz) + (cz)/(ax + by+cz) = a/(a+x) + b/(b+y) + c/(c+z)` or, `(ax+by+cz)/(ax+by+cz) = a/(a+x) + b/(b+y) + c/(c+z)` or, ` 1 = a/(a + x) + b/(b + y) + c/(c +z)` ` :. a/(a +x) + b/(b=y) + c/(c+z) = 1` |
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| 82. |
If ` x : a = y : b = z : c `, then prove that `x^(3)/a^(2) + y^(3)/b^(2) + z^(3)/c^(2) = ((x+y+z)^(3))/((a+b+c)^(2))` |
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Answer» Given that ` x : a = y : b = z : c` or, ` x/a = y/b = z/c = k (k ne 0) `(let) ` :. X = ak, y = bk , z = ck`. LHS `= x^(3)/a^(2) + y^(3)/b^(2) + z^(3)/c^(2) = ((ak)^(3))/a^(2) + ((bk)^(3))/b^(2) + ((ck)^(3))/c^(2)` ` = (a^(3)k^(3))/a^(2) + (b^(3) k^(3))/b^(2) + (c^(3)k^(3))/c^(2) = ak^(3) + bk^(3) + ck^(3)` ` = k^(3) (a + b + c)`. RHS ` = ((x+y+z)^(3))/((a+b+c)^(2)) = ((ak+bk+ck)^(3))/((a+b+c)^(2))` ` = ({k(a+b+c)}^(3))/((a+b+c)^(2))= (k^(3)(a+b+c)^(3))/((a+b+c)^(2)) = k^(3)(a+b+c)`. ` :. ` LHS = RHS |
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| 83. |
If mean - proportional of (x - 2) and (x - 3) be x, then the value of x is _________ . |
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Answer» The mean- proportional of (x -2) and (x - 3) is x. ` :. ` by definition , ` (x -2)/x = x/(x -3)` or, ` x^(2) - 2x - 3x + 6 = x^(2)` or, ` -5x + 6 = 0 " or, " -5x = - 6`. or, ` x = (-6)/(-5) " or, " x = 6/5 = 1 1/5` Hence the value of x is ` underline (1 1/5)`. |
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| 84. |
If ` x : a = y : b = z : c `, then prove that `(a^(2) + b^(2) + c^(2))(x^(2) + y^(2) + z^(2)) = (ax + by + cz)^(2)` |
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Answer» Given that ` x : a = y : b = z : c` or, ` x/a = y/b = z/c = k (k ne 0) `(let) ` :. X = ak, y = bk , z = ck`. LHS `(a^(2)+b^(2)+c^(2))(x^(2)+y^(2)+z^(2))` ` = (a^(2) + b^(2) + c^(2)){(ak)^(2)+(bk)^(2)+(ck)^(2)}` ` = (a^(2) + b^(2) + c^(2))(a^(2)k^(2)+b^(2)k^(2)+c^(2)k^(2))` ` = (a^(2) + b^(2) + c^(2))* k^(2) (a^(2)+b^(2)+c^(2)) = k^(2) (a^(2)+b^(2)+c^(2))^(2)` RHS ` = (ax + by + cz)^(2) = (a.ak+b.bk + c.ck)^(2)` ` = (a^(2)k + b^(2)k + c^(2)k)^(2) = {k(a^(2) + b^(2) +c^(2))}^(2)` ` = k^(2) (a^(2)+b^(2)+c^(2)) ` ` :. ` LHS = RHS |
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| 85. |
If `a/2 = b/3 = c/4 = (2a - 3b + 4c)/p`, then find the value of P . |
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Answer» `a/2 = b/3 = c/4 = (a xx 2 - b xx 3 + c xx 4)/(2 xx 2 - 3 xx 3 + 4 xx 4)` ` = (2a - 3b + 4c)/(4 - 9 + 16) = (2a - 3b + 4c)/11` ` :. a/2 = b/3 = c/4 = (2a - 3b + 4c)/11 = (2a - 3b + 4c)/p` ` :. p = 11`. |
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| 86. |
A is a positive number and if ` a : 27/64 = 3/4 : a`, then the value of a will beA. `81/(256)`B. 9C. `9/16`D. `16/9` |
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Answer» Correct Answer - C Given that ` a : 27/64 = 3/4 : a` or, `a/((27)/(64)) = (3/4)/a " or," a^(2) = 27/64 xx 3/4` or, ` a^(2) = 81/(256)` or, ` a = sqrt(81/256) =sqrt((9/16)^(2)) = 9/16`. `:. ` (c ) is correct. |
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| 87. |
If `a : b = c : d = e : f`, then prove that ` (a^(2) + c^(2) + e^(2)) (b^(2)+d^(2)+f^(2)) = (ab + cd + ef)^(2))` |
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Answer» Given that ` a : b = c : d = e : f` or, `a/b = c/d = e/f = k " (let)" ( k ne 0)` ` :. A = bk , c = dk " and " e = fk`. Now, LHS ` = (a^(2) + c^(2) + e^(2)) (b^(2) + d^(2) + f^(2))` ` = {(bk)^(2) + (dk)^(2) + (fk)^(2)} (b^(2) + d^(2) + f^(2))` ` = (b^(2)k^(2) + d^(2) k^(2) + f^(2) k^(2))(b^(2) + d^(2) + f^(2))` ` = k^(2) ( b^(2) + d^(2) + f^(2)) (b^(2) + d^(2) + f^(2))` ` = k^(2) (b^(2)+d^(2)+f^(2))^(2)` RHS ` = (ab+cd+ef)^(2) = (bk.b + dk.d + fk.f)^(2)` ` = (b^(2)k+d^(2)k+f^(2)k)^(2) = {k(b^(2)+d^(2) +f^(2))}^(2)` ` = k^(2) (b^(2) +d^(2)+f^(2))^(2)`. ` :. ` LHS = RHS |
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| 88. |
If the product of three continued proportional positive numbers be 64, then their mean proportional is _____ . |
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Answer» Let the three positive numbers which are in continued proportional be a, b, c. ` :. a/b = b/c " or, " b^(2) = ac ` ………….(1) As per question, `abc = 64 " or, " b xx ac = 64` or, ` b xx b^(2) = 64 " or, " b^(3) = 4^(3) = 4^(3) :. B = 4`. ` :. ` the required mean - proportion is `underline4` |
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| 89. |
If a, b, c, d are in continued proportion, then prove that ` (b -c)^(2) + (c -a)^(2) + (b-d)^(2) = (a -d)^(2)` |
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Answer» Since a,b,c,d are in continued proportion, ` a/b = b/c = c/d = k " (let)" [k ne 0]` ` :. A = bk, " "b = ck, " "c = k` ` = ck.k" =dk.k` ` = ck^(2) " "= dk^(2)` ` = dk.k^(2)` ` = dk^(3)` Now, LHS ` = (b-c)^(2) + (c - a)^(2) + (b -d)^(2)` ` = (dk^(2) - dk)^(2) + (dk - dk^(3))^(2) + (dk^(2)-d)^(2)` ` = d^(2) k^(4) - 2d^(2) k^(3) + d^(2)k^(2) + d^(2)k^(2) - 2d^(2)k^(4) + d^(2)k^(6) + d^(2)k^(4)-2d^(2)k^(2)+d^(2)` ` = d^(2)k^(6) - 2d^(2)k^(3)+d^(2)` RHS ` = (a-d)^(2)` ` = (dk^(3)-d)^(2)` ` = d^(2)k^(6) - 2d^(2)k^(3) +d^(2)` ` :. ` LHS = RHS . |
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| 90. |
If `2a = 3b = 4c`, then ` a : b : c` will beA. `3 : 4 : 6`B. `4 : 3 : 6`C. `3 : 6 : 4`D. `6 : 4 : 3` |
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Answer» Correct Answer - D Given that `2a = 3b = 4c " or, " a/(1/2)= b/(1/3) = c/(1/4)` ` :. A : b : c = 1/2 : 1/3 : 1/4 = 6 : 4 : 3` [multiplying by 12] ` :.` (d) is correct. |
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| 91. |
If ` a : b = b : c`, then prove that `a^(2)b^(2)c^(2) = (1/a^(3) + 1/b^(3) + 1/c^(3)) = a^(3) + b^(3) + c^(3)` |
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Answer» Given that ` a : b = b : c` ` rArr a/b = b/c = k " (let)", [k ne 0]` ` :. A = bk = ck.k = ck^(2) " and " b = ck`. LHS ` = a^(2)b^(2)c^(2) (1/a^(3)+1/b^(3)+1/c^(3))=(b^(2)c^(2))/a + (c^(2)a^(2))/b+(a^(2)b^(2))/c` ` = ((ck)^(2).c^(2))/(ck^(2)) + (c^(2)(ck^(2))^(2))/(ck) + ((ck^(2))^(2)* (ck)^(2))/c` ` = c^(3) + c^(3) k^(3) + c^(3) k^(6) = c^(3) (1+k^(3)+k^(6))` RHS `= a^(3) + b^(3) + c^(3) = (ck^(2))^(3) + (ck)^(3) + c^(3)` ` = c^(3) + c^(3) + c^(3) k^(6) = c^(3) (1 + k^(3) + k^(6))` ltbr. ` :. ` LHS = RHS |
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| 92. |
`x^(3)y, x^(2)y^(2) " and " xy^(3)` are in continued proportional. |
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Answer» The given three quantities are `x^(3) y, x^(2)y^(2) " and " xy^(3)`. Now, `(x^(3)y)/(x^(2)y^(2)) = x/y , " Also, " (x^(2)y^(2))/(xy^(3)) = x/y` i.e., `(x^(3)y)/(x^(2)y^(2)) = (x^(2)y^(2))/(xy^(3))` ` :. ` The given quantities are in continued proportional. Hence the statement is true . |
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| 93. |
If ` a : b = b : c`, then prove that `(abc(a+b+c)^(3))/((ab+bc+ca)^(3)) = 1` |
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Answer» Given that ` a : b = b : c` ` rArr a/b = b/c = k " (let)", [k ne 0]` ` :. A = bk = ck.k = ck^(2) " and " b = ck`. LHS ` = (abc (a + b + c)^(3))/((ab+bc + ca)^(3) ) = (ck^(2).ck.c(ck^(2)+ck+c)^(3))/((ck^(2).ck+ck.c + c.ck^(2))^(3))` `= (c^(3)k^(3){c(k^(2)+k+1)}^(3))/((c^(2)k^(3)+c^(2)k+c^(2)k^(2))^(3))=(c^(6)k^(3)(k^(2)+k+1)^(3))/(c^(6)k^(3)(k^(2)+k+1)^(3)) = 1` RHS = 1. ` :. ` LHS = RHS . |
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| 94. |
The compound ratio of the ratios `ab : c^(2), bc : a^(2) " and " ca : b^(2) " is " 1 : 1`. |
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Answer» The compound ratio of the ratios ` ab : c^(2), bc : a^(2) " and " ca : b^(2)` ` = (ab xx bc xx ca) : (c^2) xx a^(2) xx b^(2))` ` = a^(2)b^(2)c^(2) : a^(2)b^(2)c^(2)` ` = 1 : 1`. Hence the statement is true. |
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| 95. |
In a school, there are 720 students. If there are 300 boys, then find the ratio of the number of girls to that of boys. |
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Answer» Correct Answer - ` 7: 5` (i) 2,3, 2016, 2019 ` 2xx 2019 = 4038 ` ` 3 xx 2016= 6048` ` 2xx 2019 ne 3 xx 2016` Hence, 2,3, 2016 and 2019 are not in proportion. (ii) 12 , 15 , 32 , 40 ` 12 xx 40 = 480` ` 15 xx 32 = 480` ` 12 xx 40 = 15 xx 32` Hence, 12, 15 , 32 and 40 are in proportion. |
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| 96. |
Which of the following statement (s) is ? Are ture? (A) Ratio has no units (B) a :b is the same as b:aA. only AB. only BC. A and BD. Neither A nor B |
| Answer» Correct Answer - A | |
| 97. |
The monthly incomes of A and B are inthe ratio of 5 : 4, their monthly expenses are in the ratio of 19 : 21, andtheir monthly savings are in the ratio of 37 : 18. If the total annualsavings of A and B is Rs. 66000, As monthly income is`R s .6000`b. `R s .7050`c. `R s .8000`d. `R s .9000` |
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Answer» I-income, E-expenses and Savings-S Let, `I_a=5x and i_b=4x` `E_a=19y and E_b=21y` `S_a=37z and S_b=18z` Annual total savings=66000,monthly total savings=5500 `5500=37z+18z; z=100` `5x-19y=3700 and 4x-21y=1800` Solving these two equations by the method of substitution we get `x=1500`, monthly income of `A= 5x=1500=7500` |
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| 98. |
If `x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl-m^(2))`, then prove that `lx + my + nz = 0`. |
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Answer» `x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl - m^(2)) = k " (let)" [k ne 0]` ` :. x = k (lm - n^(2)), y = k (nm - l^(2)), z = k (ml - m^(2))` or, ` lx = k (l^(2)m - n^(2)l), my = k (m^(2)n - l^(2)m), nz = k (n^(2) l - m^(2)n)` or, `lx + my + nz = k(l^(2) m - n^(2)l + m^(2)n - l^(2)m + n^(2)l - m^(2)n)` ` = k xx 0 = 0`. ` :. lx + my + nz = 0`. |
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| 99. |
If we distribute 57 chocolates to three friends, A,B and C in the ratio respectively, then find the number of chocolates received by C.A. 19B. 27C. 24D. 15 |
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Answer» Correct Answer - B LCM of 3,2 and 4 =12 The ratio of number of chocolates distributed to A,B and C `1/3 : 1/2 : 3/4 = 1/3 xx 12 : 1/2 xx 12 : 3/4 xx 1` = 4:6:9 The number of chocolates received by ` C= 9/((4+6+9)) xx 57 9/18 xx 57 = 27` Hence, the correct option is (b). |
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