Question

the ratio of the income of two persons in 11:7 and the ratio of there expenditure is 9:5. if each of them managers to save rs 400 per month. find their total income.​

Answer 1

Answer:

∴ The incomes of two persons is Rs. 2200 and Rs. 1400 respectively

Step-by-step explanation:

Given:

• The ratio of the income of two persons in 11:7 and he ratio of there expenditure is 9:5.
• If each of them manages to save Rs. 400 per month.

To find:

• Their total income

Solution:

Let the income of two persons be 11x and 7x and the ratio of there expenditure be 9y and 5y.

We know that each of them manages to save Rs. 400 per month.

So, subtract expenditure from their income which is equal to money saved by both.

• 11x - 9y = 400
• 7x - 5y = 400

By using elimination method,

• ( 11x - 9y = 400 ) × 7
• ( 7x - 5y = 400 ) × 11

• 77x - 63y = 2800. ....1
• 77x - 55y = 4400. ...2

Now, subtract eq2 from eq1, we get:

• 77x - 63y - ( 77x - 55y ) = 2800 - 4400
• 77x - 63y - 77x + 55y = 2800 - 4400
• 77x - 63y - 77x + 55y = 2800 - 4400
• - 63y + 55y = - 1600
• - 8y = - 1600
• y = -1600/-8
• y = 200

Now, find out x

• 7x - 5y = 400
• 7x - 5 × 200 = 400
• 7x - 1000 = 400
• 7x = 400 + 1000
• 7x = 1400
• x = 1400/7
• x = 200

∴ The incomes of two persons = 11 × 200 = Rs. 2200 and 7 × 200 = Rs. 1400 respectively.

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