Formulate the following problems as a pair of equations, and hence find their solutions:
One number is greater than thrice the other number by 2. If 4 times the smaller number exceeds the greater by 5, find the numbers.

Question

Formulate the following problems as a pair of equations, and hence find their solutions:
The ratio of income of two persons is 9: 7 and the ratio of their expenditure is 4: 3. If each of them manages to save ₹ 2000 per month, find their monthly income.

Philoid · Accepted Answer

Let the incomes be x and expenditure be y.

We know that savings = income – expenditure

First condition is

9x – 4y = 2000

Second condition is

7x – 3y = 2000

For cross multiplication method, we write the coefficients as

Hence, we get = =

⇒ = =

⇒ x = 2000

⇒ y = 4000

∴ Income of first person = 9x = 9 × 2000 = Rs. 18, 000

Income of second person = 7x = 7 × 2000 = Rs. 14, 000