RATIO AND PROPORTION

Ratio between 200 gm and 4000 gm

=200/4000 gm

=1/20 gm

correct answer =1:20

L.C.M of 3,8 and 6 is (2*2*2*3)=24

1/3 : 1/8 : 1/6

= 1*24/3 : 1*24/8 : 1*24/6

= 8 : 3 : 4

Correct answer is 8 : 3 : 4

The inverse ratio of 11:15 is

Correct answer is  15 : 11

The ratio compound of the two ratios a : b and  c : d is ac : bd

2 : 3, 9 :4, 5 : 6 and 8 : 10 is

2 : 3 and 9 :4

so that 2*9 : d 3*4

= 18 : 12

= 3 :2

5 : 6 and  8 : 10

=5*8 : 6*10

=40 : 60

2 : 3

The compound ratio 3 : 2 and 2 : 3

=3*2 : 2*3

=6 : 6

1 : 1 is correct answer

The triplicate ratio of 2:3 is

=2³ : 3³

=8 : 27 is correct answer

A ratio compounded of itself is called its duplicate ratio. (a² : b²)

duplicate ratio of 3 : 4 is

=3² : 4²

=9 : 16

The ratio compounded of 4 : 9

The compounded ratio of the  two ratio a : b and c : d is ac : bd

=4 : 9 and 9 : 16

=4*9 : 9*16

=36 : 144

=36/144

=1:4 is correct answer

If a : b = 3 : 4, the value of (2a 3b) : (3a 4b) is

a= 3 , b = 4

(2a 3b) : (3a 4b)

=(2*3 3*4) : (3*3 4*4)

=(6 12) : (9 16)

18 :  25 is the correct answer

The angles of a triangle are in ratio 2 : 7 : 11. The angles are

Let assume angle is =x

sum of angle =180

2x 7x 11x =180

20x=180

x=180/20

x=9

2(9) : 7(9) : 11 (9)

angles of triangle  is  18⁰ : 63⁰ : 99⁰

The ratio of two number is 7 : 10 and their difference is 105. The numbers are

Two number 7 and 10

let the number is = x

equation is

7x-10x =105

-3x=105

x=105 /3

x=35

7x : 10x

7(35) : 10 (35)

245 : 350

If x : y =3 :4, the value of x²y xy² : x³ y³ is

x = 3, y = 4

x²y xy² : x³ y³

(3)²(4) (3)(4)² : (3)³ (4)³

(3*3*4) (3*4*4) : (3*3*3) (4*4*4)

36 48 : 27 64

84 : 91

12: 13 is correct answer

The mean proportional between 25,81 is

Mean proportional between = a and b

a=25, b=81

Mean proportional= √25*81

=√2025

The mean proportional between 25, 81 is =45

The third proportional to 12, 18 is

a= 12, b=18

a : b and b: c

12 : 18 and 18 : c

b² = 12*c

324 = 12* c

C =27

If A=B/2 =C/5, then A : B : C is

A=1

B=B/2

C=C/5

A/1 : B/2 : C/5

1 : 2 : 5

(5x – 3y) / (5y -3x ) =3 / 4

4 (5x -3y ) = 3(5y – 3x )

20x – 12y = 15y – 9x

20x 9x = 15y 12y

29x = 27y

x / y =27 /29

x : y =27 : 29

Answer not match

Division of Rs. 750 into 3 parts in the ratio 4 : 5 : 6 is

the ratio 4 : 5 : 6 is= x

4x 5x 6x=750

15x=750

x=750/15

=50

3 parts

4*50 : 5*50 : 6*50

200 : 250 : 300

12, 16, * , 20 are in proportion. Then * is

let assume * is =x

a=12 , b=16, c= x, d =20

a/b=c/d i.e ad=bc

12*20 = 16 * x

240 =16 * x

x = 16 / 240

x=15

The mean proportional between 1.4 gms and 5.6 gms is

Mean proportional between = a and b

a=1.4 gms, b=5.6 gms

Mean proportional= √1.4 * 5.6

=√7.84

The mean proportional between 1.4 gms and 5.6 gms  is =2.8

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 Km. in 5 hours, the speed of the first train is Speed = Distance/ Time

2nd train  speed = 400/5

= 80 km/hr

that mean 80 =8

80/8=10

=10*7

= 70 km/hr

a : b =c: d =a-c : b-d

(a/b = c/d = a-c/b-d)