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Question

The ratio incomes of two person is 9:7 and the ratio of their expenditures is 4:3. If each them manages to save Rs. 2000 per month, find their monthly income.


Solution

The ratio of incomes of two persons is 9:7 Let their incomes be Rs. 9x and Rs . 7x The ratio of their expenditures is 4:3 Let their expenditure be Rs. 4y and 3y From the problem 9x - 4 y = 2000 .......... (1) 7x - 3y = 2000 ............(2) 
The equation (1) $$\times7 and (2) \times 9,$$ we get 
63x - 28 y = 14000........(3) and 63x - 27 y =  18000 ......... (4) The equation (3) - (4) , we get 
$$-y = -4000\Rightarrow y = 4000$$Substitute y value in the equation (1) 
$$\Rightarrow 9x - 16000 = 2000$$$$\Rightarrow9x = 2000+16000=18000$$$$\Rightarrow x=\dfrac{18000}{9}=2000\Rightarrow Rs.2000$$ $$9x=9\times Rs.2000=Rs.18000$$
$$7x=7\times Rs.2000=Rs.14000$$
$$\therefore$$ Their incomes are Rs . 18000 and Rs. 14000

Mathematics

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