Question

The annual income of Rahul and Mohit are in the ratio 17 : 12 and the ratio of their expenditure is 5 : 3. If each of them saves Rs 9000 yearly, then what will be the annual income (in Rs) of Mohit?

Answer 1

Given:

The annual income of Rahul and Mohit are in the ratio 17:12

The ratio of their expenditures is 5:3

Saving of each person = Rs. 9000

Now,

Let the income of Rahula and Mohit be 17x, 12x respectively.

And their expenditures be 5y, 3y respectively.

Then,

The linear equations we get -

17x - 5y = 9000 ------(i)

12x - 3y = 9000 ------(ii)

• BY ELIMINATION METHOD

We will make the coefficients of x numerically equal in both equations.

On multiplying Eq(i) by 12 and Eq.(ii) by 17, we get,

204x - 60y = 108000 ------(iii)

204x - 51y = 153000 ------(iv)

$Now,$

By subtracting equation(iv) from equation(iii), we get,

   204x - 60y = 108000 ------(iii)

   204x -  51y =  153000 ------(iv)

(-)          (+)        (-)  

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               -9y = - 45000

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$So,$

⇒ -9y = -45000

⇒ y = -45000 ÷ (-9)

⇒ y = 5000

On putting y = 5000 in eq.(i), we get,

17x - 5(5000) = 9000 ------(i)

⇒ 17x - 25000 = 9000

⇒ 17x = 9000 + 25000

⇒ 17x = 34000

⇒ x = 34000 ÷ 17

⇒ x  = 2000

Therefore,

The annual income of

Rahul = 17x = 17(2000) = Rs.34000

And Mohit = 12x = 12(2000) = Rs.24000

$Hence,$

The annual Income of Mohit is Rs. 24000

• BY CROS MULTIPLICATIONMETHOD

The equations-

17x - 5y - 9000 = 0 ------(i)

12x - 3y - 9000 = 0 ------(ii)

Here,

$a_1 = 17\ ;\ a_2 = 12$

$b_1 = (-5)\ ;\ b_2 = (-3)$

$c_1 = (-9000)\ ;\ c_2 = (-9000)$

Now,

$\boxed{x = \frac{b_1 c_2 - b_2 c_1}{a_1 b_2 - a_2 b_1}}$

$\bf x = \frac{[(-5)(-9000)] - [(-3)(-9000)]}{17(-3) - 12(-5)}$

$\bf x = \frac{(45000) - (27000)}{(-51) - (-60)}$

$\bf x = \frac{(18000)}{-51+60}$

$\bf x = \frac{(18000)}{9}$

$\therefore \boxed{\bf x = 2000}$

Now,

$\boxed{y = \frac{c_1 a_2 - c_2 a_1}{a_1 b_2 - a_2 b_1}}$

$\tt y = \frac{[(-9000)(12)] -[(-9000)(17)]}{17(-3) - 12(-5)}$

$\tt y = \frac{-108000 - (-153000)}{-51+60}$

$\tt y = \frac{45000}{9}$

$\therefore \boxed{\bf y = 5000}$

So,

The annual income of Mohit = 12x = 12(2000) = Rs. 24000

Answer 2

Answer:

Rs 24000

Step-by-step explanation:

Take

Rohit income = 17x

Mohit income = 12x

Their expenditures

Rohit = 5y

Mohit = 3y

And make linear equation

17x - 5y = 9000

12x - 3y = 9000

And there are methods

elimination, cross multiplication, substitution

By cross multiplication

find x = b1c2 - b2c1 / a1b2 - a2b1

we will get 2000 by further solving

So,

Mohit income = 12x = 12 * 2000 = Rs 24000