C6 9Gmtn 10001

9Math Q06-1001
Chapter 6
Ratio, proportion and Variation

1. 4 gallons : 6 quarts=……….
   A. 2:3 B. 8:3 C. 4:6 D. 3:8 E. None of these
2. 6600 feet : 2 miles =…………
   A. 8:5 B. 5:8 C. 33:1 D. 22:1 E.3300:1
3. If 12x+y=2x, then x:y=……….
   A. 1:2 B. 2:3 C.3:4 D. 3:5 E. 4:5
4. The ratio 27:36 , expressed as a percentage, is
   A. 25% B. 45% C. 60% D. 75% E. 80%
   5.The ratio 2:x , expressed as a percentage , is 40%, then x=………..
   A. 3 B. 4 C.5 D. 6 E.8
5. If a:b=3:8 and b:c=4:5, then a:c=…………..
   A. 5:11 B. 3:8 C. 3:11 D. 3:10 E. 5:8
6. If a:b=3:5 and b:c=3:5, then a:b:c=………
   A. 2:3:5 B.3:5:7 C.6:10:15 D. 9:15:25 E.9:20:27
7. If a:b = 5:3 , then 3a+ 4b: 4a+3b is
   A. 27:36 B. 29:27 C. 27:29 D. 26:29 E. 17:19
8. If 2x +3y:2x+y=3:2, then x:y=……….
   A. 3:2 B. 2:3 C. 4:3 D. 3:4 E. None of them
9. The cost of 40 pens is k. 360 and the cost of 30 pencils is k. 90. The ratio of the cost of a
   pen to that of a pencil is
   A. 1:3 B. 1:4 C. 3:1 D. 4:1 E. 16:3
10. The ratio of the area of a circle of radius 7 cm to the area of a circle of radius 14 cm is
    A. 1:2 B. 2:3 C. 3:5 D. 4:9 E. 1:4
11. If the ratio of the areas of two circles is 49:25 , then the ratio of the diameters of these
    circles is
    A. 3:4 B. 4:5 C. 7:5 D. 6:5 E. 1:4
12. If x is 23 of y and y is 34 of z , then the ratio of z to x is
    A. 2:1 B. 1:1 C. 3:2 D. 1:2 E. 4:3
13. If 2x2 -5xy + 3y2=0, then x:y=……….
    A. 2:5 B. 5:3 C. 1:1 D. 1:1 (or) 2:3 E. 3:2 (or) 1:1
14. If xy = x + y, where x and y are real numbers, then y cannot be
    A.0 B.1 C. -1 D.2 E. -2
15. If 3a = 4b = 5c, then 1a:1b:1c =…………
    A. 13:14:15 B.15 :14: 13 C. 14:15:13 D. 3:4:5 E.5:4:3
16. If x:y:z =2:3:4 and x + y +z = 18 , then xyz = …………
    A.12 B.48 C.192 D.256 E.512
17. If (5x-4y) = 4(2x-3y) , then x : y = ……….
    A. 3:8 B. 8:3 C. 12: 17 D. 6:-13 E. 13:18
18. If x:y = 2:3 , find (x2 + y2):(x2-y2).
    A. 2:5 B. 13:-5 C.6:13 D. 6:-13 E. (9:13)
    20.Let x,y,z be three unequal numbers . Which of the following is (are) equal to x:y:z?
    1.5x: 5y : 5z 2. x+1 : y+1 : z+1 3. x2 : y2 : z2
    A.1 only B. 2 only C. 1 and 2 only D. 2 and 3 only E. 1,2 and 3

21.Divide k. 340 into 3 parts such that their ratios are 12:13:19, then the largest part is
A. k. 170 B. k.180 C. k. 192 D. k.184 E. 200

1. ∠P:∠Q:∠R = 3:4:5, S=………….
   A.45° B.60° C.75° D.90° E. It cannot be found

2. A sum of money is to be shared among three persons A, B , C in the ratio 1:12:13 money. If A
   gets k.720, find the sum of the money.
   A. k. 1320 B. k.1440 C.k.1670 D. k.3960 E.k.4320

3. If 1a:1b=3:4 and a:c =2:5 , then a:b:c =………
   A.3:4:5 B.2:3:4 C. 4:3:5 D.3:4:10 E. 4:5:6

4. If a:b = 2:3, b:c = 5:3 , then a-b+ca+b-c =……….
   A.12 B. 52 C.4 D.14 E.14
   26.The measure of the angle of a quadrilateral are in the ratio 1 : 2 : 3 : 4, then the degree
   measure of the largest angle is
   A.36° B.45° C.90° D.108° E.144°

5. If k.1800 is divided into three amounts in the ratio 4:5:6. The largest amount is
   A. k.900 B. k.720 C. k.600 D.k.480 E.k.390

6. A sum of money is divided among A, B and C in the ratio 7:3:2 . A has k.36 more than B,
   C has
   A. k.9 B.k.12 C. k.18 D. k.27 E.k.21

7. The mean proportional between 9 and 16 is
   A.6 B.1212 C.12 D.±12 E.±1212
   30.If ab+c =bc+a=ca+b, and provided that a+b+c≠0, then each ratio is
   A.0 B.1 C. 2 D.12 E .None of them

8. The lengths of the sides of a triangle similar to a triangle with sides 8,12,16 ft long with the
   twice area are
   A. 83 ,123,163 B.2,3,4 C. 16,24,32 D. 82,122,162 E.22,32,42

9. If y varies inversely as the cube of (x+1) and k is the constant of proportionality, then
   A. y = kx3 + 1 B. y=k(x+1)3 C. y= kx3+1 D. y= kx+13 E. y=1x+13 +k

10. z varies directly as x and inversely as the square of y, then
    A. z ∝ xy2 B. z∝ yx C. z∝ xy2 D. z∝ xy E. z∝yx

11. Given that xy2 is constant and x=3, when y=4, the value of x when y=8 is
    A. 43 B.34 C.38 D.83 E.12

12. It is given that y=kx and that 20≤x≤100 . If the smallest value of y is 30, the value of k is
    A.200 B.2000 C.300 D. 3000 E.600

13. If xy+x=yx+z=zx+y then each ratio=……….
    A. 12 B.1 C. 1 or 0 D. 12 or -1 E. -12 or 1

14. V varies as T and inversely as P. The constant of variation when T= 360, P = 736 and
    V = 450 is
    A. 450 B.736 C. 920 D.810 E. 360

15. If x varies directly as y and inversely as square of z and that x =10 when y=4 and z=14.
    Then when y= 16 and z= 7 ,x=……….
    A. 180 B.160 C.154 D.140 E.120

16. The sum of three constitutive integers is 54. The largest number is
    A. 16 B.20 C.8 D.19 E.17

x 1 2 3 4 6 10
y 6 3 2 1.5 1 0.6

The table shows the variation of y with respects to x . The constant of variation k is
A. 0.06 B. 16 C. 23 D. 32 E. 6

1. P varies directly as x and inversely as the square of y. If x is decreased by 30% and y is
   decreased by 20% , the percentage change in p is
   A. increase 10% B. decrease 10% C. increase 9.4% D. decrease 9.4% E.N0. change
2. Let x varies inversely as y2 and y varies directly as z .Which of the following is (are) true?
   1.xy2= constant 2. = y2z= constant 3. xz= constant
   A. 1 only B. 2 only C. 3 only D. 2 and 3 only E. 1,2 and 3
3. If x varies directly as y2 and inversely as z. Find the percentage increase of x when y is
   increase by 25% and z is decreased by 20%,
   A. 5% B.50% C.85% D.95% E.100%
4. If x varies directly as y and inversely as square of z and that x= 10 when y=4 and z=14
   Then y=16 and z=7, x=………..
   A.180 B.160 C. 154 D. 140 E. 120
5. If the surface area of a sphere increases by 44%, its volume increase by
   A. 20% B. 23.1% C. 60% D. 66% E.72.8%

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Thank you!