RATIO & PROPORTION (9/10)

                      RATIO
EXAMPLE)
find the comounded ratio of 4/5 and 10/9
Solution)
4/5 . 10/9= 40/45= 8/9 ans

Example) find the duplicate ratio of a²: b
Sol)
Duplicate of a²:b is (a²)²: b²
a⁴: b².  Ans)

Ex) find triplicate of a:b²
Sol)
Triplicate of a: b² = (a)³: (b²)³
a³: b^6.  Ans)

Ex) Find the subduplicate of 4:9

Sol) √4: √9
= 2:3. Ans

Ex) If a:b= 2:3, find (2a+3b)/a-b)
Sol)
Let a:b= 2:3= k
a/b = 2/3= k
a/2= b/3= k
a=2k and b= 3k
Now putting ( 2.2k+3.3k)/(2k+3k)
=7k/5k
=7/5.  Ans

Example) If (2x+3y)/(2x-3y)= 2/3. Find (3x+y)/(x+y)
Sol) (2x+3y)/(2x-3y)= 2/3
Or, 6x+ 9y= 4x -6y
Or, 2x= -25y
x/-25= y/2= k let
x= -25k and y= 2k
Putting (3.-25k+3.2k)/(2.-25k- 3.2k)
= -69k/+44k
= 69/44. Ans.

Exercise)

A) find the compound ratio of:
1) 2/3, 3/4, 4/5
2) 4:5, 5:6, 6:7
3) 2a:3b, 6b:5a, 5a:b
4) (a+b)/(a-b), (a²-b²)/(a²+b²), (a²-2ab+b²)/(a²+2ab+b²)
5) 3a: 5b , 2b: 3a

B) find the duplicate of:
1) 5:7
2) a²: b³
3) √a : b²

C) Find the triplicate of:
1) 3:5
2) (x+y)^1/3: (x -y)^1/3

D) find the subduplicate of:
1) a⁴: b²
2) 16: 25
3) (a²+2ab+b²):(a² -2ab+b²)

E) find subtriplicate of:
1) 27: 8
2) a³: b³
3) 27:64
4) (a-b)³: (a+b)³

F)
1) If a:b= 7:8 find ( a+3b)/(2a-3b)
2) if a:b = 2: 5 find
(4a- b/2):(4a+ b/2)
3) a) If x:y=9/10 find
(5x+3y)/(5x -3y)
b) (2x²+3y²)/(2x² - 3y²)
4) if a:b= 7:5 find (7a-2b)/(7a+3b)
5) if 2a:b= 3:4 find (8a-b)/(8a+b)

G)
1) If (3a²+2b²)/(3a²- 2b²)= 11/9 find (3a⁴+25b⁴)/(3a⁴- 25b⁴)

2) If (5x - 11y)=(2x +5y) find the value of (3x²+2y²)/(3x²- 2y²)

3) If (5x+4):(3x -5) is the duplicate ratio of 2:3, find x

4) If (6x-5): (7x -8) is the triplicate ratio of 3:2 find the value of x.

5) Two numbers are in the ratio of 8:5 and the difference of their squares is 156. Find the numbers.

6) Two numbers are in the ratio of 1/3 : 1/2 and the difference of their squares is 80. Find the numbers.

7) If 7A= 5B and 6B= 7C find A:C

8) If 11a= 7b, 8b= 9c, 29c= 11d, find a/d

9) If (x+3): (2x -1) is the duplicate ratio of 4:5 find x

10)If (2x -2): (4x +7) is the triplicate ratio of 2:3 find x.

11) If x:y = 4:5, find the ratio of (5x-3y): (2y +15x)

12) If 12(2x²- 3y²)= 8x² - 11y², find (4x+y): (4x -y)

13) If x/y = 5/7, find (3x+2y)/(3x-2y)

14) If x/y = 4/9; find (9x-4y)/(9x+4y)

15) If x/y= 5/9; find the value of (2x²-3y²)/(2x²+3y²)

16) If x/y= 7/10; find the value of (5x+7y)/(5x- 7y)