A) 18000, 14000
B) 20000,12000
C) 22000,10000
D) None of the above
Correct Answer: A
Solution :
Given, ratio of incomes \[=9:7\] |
and ratio of their expenditures \[=\text{ }4:3\] |
Saving of each person = Rs 2000 |
Let incomes of two persons be 9 x, 7x and |
their expenditures be 4y, 3y. |
Then, linear equations so formed are |
\[9x-4y=2000\] (i) |
And \[7x-3y=2000\] |
We make the coefficients of x numerically equal in both equations. On multiplying |
Eq.(i) by 7 and Eq. (ii) by 9, we get |
\[63x-28y=14000\] ...(iii) |
and \[63x-27y=18000\] ...(iv) |
On subtracting Eq. (iv) from Eq. (iii), we get |
\[-28y+27y=14000-18000\] |
\[\Rightarrow \,\,\,\,\,-y=-4000\,\,\,\,\Rightarrow \,y=4000\] |
On putting y = 4000 in Eq. (i), we get |
\[9x-4\times 4000=2000\] |
\[\Rightarrow \,\,\,\,\,9x=2000+16000\] |
\[\Rightarrow \,\,\,x=\frac{18000}{9}=2000\] |
Thus, monthly income of both persons are |
9(2000) and 7(2000), i.e. Rs 18000 and Rs 14000, respectively. |
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