Question: The monthly income of Rita and Bishwant are in the ratio of 4:3 and their expenses are in the ratio 3:2. If each of them saves Rs 2000 in a month, find their monthly income.

Solution:

Let the monthly income of Rita and Bishwant be 4x:3x.

Let the monthly expenses of Rita and Bishwant be 3y:2y.

Total savings in a month = Rs 2000

According to the question,
Total income - Total Expense = Total Savings

Now,

Total savings of Rita = Rs 4x - Rs 3y
$or, Rs 2000 = Rs (4x -3y)$
$or, 4x - 3y = 2000$
$or, 4x = 2000 + 3y$
$or, x = \frac{2000 + 3y}{4}$ - (i)

And,

Total savings of Bishwant = Rs 3x - Rs 2y
$or, Rs 2000 = Rs (3x - 2y)$
$or, 3x -2y = 2000$ - (ii)

Put value of x from equation (i) in equation (ii), we get,

$or, 3( \frac{2000 + 3y}{4}) - 2y = 2000$

$or, \frac{3(2000 + 3y)}{4} = 2000 + 2y$

$or, 6000 + 9y = 4(2000 + 2y)$

$or, 6000 + 9y = 8000 +8y$

$or, 9y -8y = 8000-6000$

$\therefore y = 2000$

Put value of y in equation (i), we get,

$or, x =  \frac{2000 + 3×2000}{4}$

$or, x = \frac{2000 + 6000}{4}$

$or, x = \frac{8000}{4}$

$\therefore x = 2000$

So, (x,y) = (2000,2000)

We have,

Monthly income of Rita = Rs 4x = Rs 4×2000 = Rs 8000
Monthly income of Bishwant = Rs 3x = Rs 3×2000 = Rs 6000

Therefore, the required monthly income of Rita and Bishwant are Rs 8000 and Rs 6000, respectively.