Question

the monthly incomes of a and b are in the ratio 4:5 and expenses are in the ratio 5:6.if a saves $250 per month and b saves $500 per month, then what are the respective incomes of a and b? ​

Answer 1

Step-by-step explanation:

Solution:

Option(A) is correct

Let A's income be = 4x

A's expenses, therefore = 4x–25

Let B's income be = 5x

B's expenses, therefore = 5x–50

We know that the ratio of their expenses = 5:6

⇒24x−150=25x−250

⇒ Therefore, x=100.

⇒A's income =4x=400 and B's income =5x=500.

Answer 2

Given: The ratio of a and b's monthly incomes = 4:5

          The ratio of a and b's expenses = 5:6

          a's savings = $250

          b's savings = $500

To find: The incomes of a and b

Solution: Let their monthly incomes be 4x and 5x.

Let their expenses be 5y and 6y.

According to the question,

4x - 5y = 250 [equation i]

5x - 6y = 500 [equation ii]

Now multiplying equation i with 5 and equation ii with 4, we get

20x - 25y = 1250 [equation iii]

20x - 24y = 2000 [equation iv]

Now subtracting iii from iv, we get

y = 750

Substituting the value of y in equation i,

4x - 5 × 750 = 250

⇒ 4x = 250 + 3750

⇒ x = 4000/4

⇒ x = 1000

Therefore, a's income = $ 4 × 1000 = $ 4000.

Amy's income = $ 5 × 1000 = $ 5000.

Answer: $ 4000 and $ 5000