﻿ Class 8 NCERT Math Solution
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TOPICS
Exercise - 2.6

Question-1 :-  Solve (8x - 3)/3x = 2 .

Solution :-
```  (8x - 3)/3x = 2
8x - 3 = 2 x 3x
8x = 3 + 6x
8x - 6x = 3
2x = 3
x = 3/2
Verification :
L.H.S = (8x - 3)/3x
= (8 x 3/2 - 3)/(3 x 3/2)
= (12 - 3)/(9/2)
= (9 x 2)/9
= 2 = R.H.S
```

Question-2 :-  Solve 9x/(7 - 6x) = 15 .

Solution :-
```  9x/(7 - 6x) = 15
9x = 15 x (7 - 6x)
9x = 105 - 90x
9x + 90x = 105
99x = 105
x = 105/99
x = 35/33
Verification :
L.H.S = 9x/(7 - 6x)
= [(9 x 35)/33] ÷ [7 - (6 x 35/33)]
= (3 x 35/11) ÷ [7 - (2 x 35/11)]
= (105/11) ÷ (7 - 70/11)
= (105/11) ÷ [(77 - 70)/11]
= 105/11 ÷ 7/11
= 105/7
= 15 = R.H.S
```

Question-3 :- Solve z/(z + 15) = 4/9 .

Solution :-
```   z/(z + 15) = 4/9
9z = 4 x (z + 15)
9z = 4z + 60
9z - 4z = 60
5z = 60
z = 60/5
z = 12
Verification :
L.H.S = z/(z + 15)
= 12/(12 + 15)
= 12/27
= 4/9 = R.H.S
```

Question-4 :-  Solve (3y + 4)/(2 - 6y) = -2/5 .

Solution :-
```  (3y + 4)/(2 - 6y) = -2/5
5 x (3y + 4) = -2 x (2 - 6y)
15y + 20 = -4 + 12y
15y - 12y = -4 - 20
3y = -24
y = -24/3
y = -8
Verification :
L.H.S = (3y + 4)/(2 - 6y)
= (-24 + 4)/(2 + 48)
= -20/50
= -2/5 = R.H.S
```

Question-5 :-  Solve (7y + 4)/(y + 2) = -4/3 .

Solution :-
```  (7y + 4)/(y + 2) = -4/3
3 x (7y + 4) = -4 x (y + 2)
21y + 12 = -4y - 8
21y + 4y = -8 - 12
25y = -20
y = -20/25
y = -4/5
Verification :
L.H.S = (7y + 4)/(y + 2)
= (-28/5 + 4) ÷ (-4/5 + 2)
= [(-28 + 20)/5] ÷ [(-4 + 10)/5]
= (-8/5) ÷ (6/5)
= (-8 x 5)/(5 x 6)
= -8/6
= -4/3 = R.H.S
```

Question-6 :-  The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

Solution :-
```   Let the age of Hari = 5x years
the age of Harry = 7x years
According to question :
(5x + 4)/(7x + 4) = 3/4
4 (5x + 4) = 3 (7x + 4)
20x + 16 = 21x + 12
20x - 21x = 12 - 16
-x = -4
x = 4
The age of Hari = 5x = 5 x 4 = 20 years
The age of Harry = 7x = 7 x 4 = 28 years
```

Question-7 :-  The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

Solution :-
```  Let the numerator of a rational number  = x
the denominator = x + 8
rational number = x/(x+8)
According to question :
(x + 17)/(x + 8 - 1) = 3/2
(x + 17)/(x + 7) = 3/2
2 (x + 17) = 3 (x + 7)
2x + 34 = 3x + 21
2x - 3x = 21 - 34
-x = -13
x = 13
The numerator of a rational number  = x = 13
The denominator = x + 8 = 13 + 8 = 23
Rational number = x/(x + 8) = 13/(13 + 8) = 13/21
```
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