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Question
Anil and Sunita have incomes in the ratio 3 : 5. If they spend in the ratio 1 : 3, each saves T 5000. Find the income of each.
Solution
Let Anil's income = Rs. x and Sunita's income = Rs. y
According to given information, we have
`x/y = (3)/(5)`
⇒ 5x = 3y
⇒ 5x - 3y = 0 ....(i)
And,
`(x - 5000)/(y - 5000) = (1)/(3)` ....[Expense = Income - Saving]
⇒ 3x - 15000 = y - 5000
⇒ 3x - y = 10000 ....(ii)
Multiplying eqn. (ii) by 3, we get
9x - 3y = 30000 ....(iii)
Subtracting eqn. (i) from (iii), we get
4x = 30000
⇒ x = 7500
⇒ 5(7500) - 3y = 0
⇒ 37500 - 3y = 0
⇒ 3y = 37500
⇒ y = 12500
Hence, Anil's income is Rs.7500 and Sunita's income is Rs.12,500.
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