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Solve: 
On multiplying both sides by 9(z + 15), we obtain
9z = 4(z + 15)
⇒ 9z = 4z + 60
⇒ 9z − 4z = 60
⇒ 5z = 60
⇒ z = 12
Solve: 
On multiplying both sides by 3x, we obtain
8x − 3 = 6x
⇒ 8x − 6x = 3
⇒ 2x = 3
⇒ 
Solve: 
cross multiplying above equation,
9x=15(7-6x)
9x=15*7-15*6x
9x=105-90x
9x+90x=105
99x=105
x=105/99=35/33
Solve: 
On multiplying both sides by 5(2 − 6y), we obtain
5(3y + 4) = −2(2 − 6y)
⇒ 15y + 20 = − 4 + 12y
⇒ 15y − 12y = − 4 − 20
⇒ 3y = −24
⇒ y = −8
Solve: 
On multiplying both sides by 3(y + 2), we obtain
3(7y + 4) = −4(y + 2)
⇒ 21y + 12 = − 4y − 8
⇒ 21y + 4y = − 8 − 12
⇒ 25y = −20
⇒ 
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.
The ratio of present ages of hari and harry=5:7
so we can assume their present ages like this
present age of hari=5k
present age of harry=7k
after 4 years, age of hari=5k+4
after 4 years ,age of harry=7k+4
(5k+4):(7k+4)=3:4
(5k+4)/(7k+4)=3/4
by performing cross multiplication,
4(5k+4)=3(7k+4)
4*5k+4*4=3*7k+3*4
20k+16=21k+12
21k-20k=16-12
k=4
present age of hari=5k=5*4=20
present age of harry=7k=7*4=28
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
. Find the rational number.
Let the numerator of the rational number be x. Therefore, its denominator will
be x + 8.
The rational number will be
. According to the question,
⇒ 2(x + 17) = 3(x + 7)
⇒ 2x + 34 = 3x + 21
⇒ 34 − 21 = 3x − 2x
⇒13 = x
Numerator of the rational number = x = 13
Denominator of the rational number = x + 8 = 13 + 8 = 21
Rational number 
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