111. 2
a + b/ a + 4b = 3 2a + b = 3 ( a +
4b) a = -11b.
A + b / a + 2b
= -11b + b /-11b + 2b = -10b / -9b = 10 /9.
112. (
2 a + 3b) (2 c – 3 d ) = (2 a – 3b) (2c + 3 d)
= (2 a + 3b) /(2 a – 3b) = (2 c + 3d ) /( 2 c -3 d) = 2 (a / b)+ 1/ (2 ( a/b ) -1= ( 2 (c/d)
+1 / 2 (c/d) – 1 a / b = c/d.
113. (
a + b + 2c + 3d) ( a – b – 2c + 3d ) = ( a – b+ 2 c – 3 d ) a + b – 2 c – 3 d)
[(a + b) + (2c + 3d)] [(a – b )
–(2 c – 3 d)]
= [( a – b ) + (2c – 3d )] [( a +b) –(2 c
+ 3 d)]
(a + b ) ( a – b ) – (a + b ) (2
c – 3d ) + ( a – b ) ( 2c + 3 d ) –(2c + 3d ) (2c – 3d)
=(a – b ) (a + b) – (a –b)
*2c + 3d ) +( a + b) (2c =3d) –(2 c + 3 d) (2 c – 3d)
( a =) (2 c – 3d ) =3bd = 2ac + 3
ad – 2bc – 3bd
4bc = 6ad 2 b c =3ad.
114. X
= y 1 – q = 2q + 1 3 q = 0 q -0.
115. X/5
– X /6 = 4. 6 X – 5X /30 = 4 X
=120.
116. 2
X – 2y = 21 / 22 X/y = (21 / 22 x 2/3) =7/11
X = 7/11 y.
4 X + 5y = 83 4 x 7/11 y + 5y = 83
28 /11 y + 5y = 83 83 y = 83 x
11 y = 11.
X = 7/11 y =( 7/11 x 11 )=7.
So, y – x = 11-7 =4.
117. 3x
= y =5 19 …(I) and X –y =9……(II)
Adding (I) and (II), we get: 4 x = 28 or X=7. Putting X = 7 in (I), we
get: y =2.
118. A
+ b =5 ….(I) and 3 a + 2b
= 20 (II)
Multiplying (I) by 2 an subtracting from (II), we get: a – 10.
Putting a = 10 in (I), we get: b = - 5.
( 3 a + b) = 3 x 10 + (-5) = 30 -5 = 25.
119. (
2p + 3q) + ( 2p – q ) = 18 + 2 4p + 2q =
20 2 ( 2p + q) =20
2p + q =10.
120. 2X
+ y = 5..(I) and 3X – 4y
=2.
Multiplying (I) by 4 and adding (II) to it, we get : 11X = 22 or x =2.
Putting
X =2 in (I), we get: y =1. So, 2xy = 2 x 2 x 2 =4.
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