We use cross multiplication in this exercise a lot of times, so it is explained here before.

Let,

a/b = c/d

Now if we multiply both sides by the denominators of left side and right side, we get,

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

=> a X d = b X c

This is called cross multiplication.

### Question.1 Solve the following equations.

**We can solve the problems 1 to 5 by trying to bring all the unknown variables to the left side.**

### 1. (8x-3) / 3x = 2

**Solution:**

By multiplying on both sides by 3x we get,

=> (8x-3) X (3x) / 3x = 2 X (3x)

=> 8x-3 = 6x

=> 8x-6x-3 = 0

=> 2x-3 = 0

=> 2x = 3

=> x = 3/2

### 2. 9x / (7-6x) = 15

**Solution:**

By multiplying both sides by (7-6x) we get,

=> (9x) X (7-6x) / (7-6x) = 15 X (7-6x)

=> 9x = (15 X 7) – (15 X 6)x

=> 9x = 105 – 90x

=> 9x + 90x = 105

=> 99x = 105

=> x = 105/99

=> x = 35/33

### 3. z / (z+15) = 4 / 9

**Solution:**

By cross multiplication,

=> z X 9 = (z+15) X 4

=> 9z = 4z + 4 X 15

=> 9z – 4z = 60

=> 5z = 60

=> z = 60/5

=> z = 12

### 4. (3y+4) / (2-6y) = 2 / 5

**Solution:**

By cross multiplication,

=> (3y+4) X 5 = (-2) X (2-6y)

=> (5 X 3)y + (4 X 5) = (-2 X 2) + (-2 X -6)y

=> 15y + 20 = -4 + 12y

=> 15y -12y = (-4) + (-20)

=> 3y = -24

=> y = -24/3

=> y = -8

### 5. (7y+4) / (y+2) = – 4 / 3

**Solution:**

By cross multiplication,

=> (7y+4) X 3 = -4 X (y+2)

=> (7 X 3)y + (4 X 3) = -4y + (-4 X 2)

=> 21y + 12 = (-4y) + (-8)

=> 21y + 4y = (-8) + (-12)

=> 25y = -20

=> y = -20/25

=> y=-4/5

### 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 present age of

Haribex,

Let the present age ofHarrybey.Presently their ages are in ratio

5:7, So we get

=> x : y = 5 : 7

We get,

=> x/y = 5/7

By cross multiplication,

=> 7x = 5y

=>x = (5y) / 7………..(1)After 4 years,

Hari’sage will bex+4,

Harry’sage will bey+4.The ratio between their ages after four years is 3:4. So we get,

=> (x+4) : (y+4) = 3 : 4

=> (x+4)/(y+4) = 3/4

By cross multiplication,

=> (x+4) X 4 = 3 X (y+4)

=> 4x +16 = 3y + 12

=>4x – 3y = -4………..(2)Now , we got two euations.

x = (5y) / 7 ……….. (1)

4x – 3y = -4 ……….. (2)If we substitute this

xvalue from(1)in equation(2)we get

=> 4 X (5y/7) – 3y = -4

=> 20y/7 – 3y = -4

=> 20y/7 – (7X3)y/7 = -4

=> (20y -21y) / 7 = -4

=> -y/7 = -4

=> y = (-4) X (-7)

=>y = 28By substituting

y=28value in(1)we get

=> x = (5 X 28) / 7

=> x = (5 X 4)

=> x =20So here

Hari’spresent age is20years and

Harry’spresent age is28years.

### 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

numeratorbex,

and thedenominatorbey.From the first part of the question we get,

=> denominator = numerator + 8

=> y = x + 8………..(1)Now, from the second part of the question ,

=> (x+17) / (y-1) = 3/2

By cross multiplication,

=> (x+17) X 2 = 3 X (y-1)

=> 2x + 34 = 3y – 3

=> 2x – 3y = -34 – 3

=> 2x – 3y = -37………..(2)We got two equations.

Substituting(1)in(2), we get

=> 2x − 3 X (x+8) = −37

=> 2x − 3x − 24 = −37

=> 37 − 24 = x

=> x = 13By substituting

x=13in(1)we get,

=> y = 13 +8

=> y = 21We got x=13 and y=21

Hence the original rational fraction will be13/21