Question

Tha ratio of the monthly income and expenditure of sunayana is 5:3 if she increases her income by 5000 and decreases the expenditure by RS 3000 the new ratio becomes 5:2 find her income and expenditure​

Answer 1

Answer:

⇒ Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y.

⇒ Now, according to question,

⇒ 3x−5y=1000 ---- ( 1 )

⇒ 2x−3y=1000 ----- ( 2 )

⇒ Now, multiplying equation ( 1 ) by 3 and ( 2) by 5.

⇒ 9x−15y=3000 ---- ( 3 )

⇒ 10x−15y=5000 ----- ( 4 )

⇒ x=2000 [Subtraction equation ( 3 ) from equation ( 4 ) ]

⇒ Then, income of A = 3x=Rs.(3×2000)=Rs,.6000.

Answer 2

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Ratio of income and expenditure=5:3

If her income increases by ₹5000 and expenditure decrease by ₹3000, the ratio will be 5:2

Let the money be x

Ratio of income and expenditure= 5x:3x

A.T.Q.

$\sf \large\frac{5x + 5000}{3x + 3000} = \frac{5}{2}$

$\sf = > 2(5x + 5000) = 5(3x + 3000)$

$\sf = > 10x + 10000 = 15x + 15000$

$\sf = > 10x - 15x = 15000 - 10000$

$\sf= > - 5x = 5000$

$\sf= > x = \frac{5000}{5} = 1000$

Her income=5x=5×1000=₹5000

Expenditure=3x=3×1000=₹3000

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