| The ratio of weekly incomes of A and B is 9: 7 and the ratio of their expenditures is 4: 3. If each saves Rs. 200 per week, then the sum of their weekly incomes in [SSC (CGL) 2011] |
A) Rs. 3600
B) Rs. 3200
C) Rs. 4800
D) Rs. 5600
Correct Answer: B
Solution :
| Let As and B's weekly incomes be Rs. \[9x\]and Rs. \[7x\]and their expenditures be Rs. \[4y\] and Rs. \[3y\]respectively. |
| \[\therefore \] \[9x-4y=200\] (i) |
| and \[7x-3y=200\] (ii) |
| \[\Rightarrow \] \[9x-4y=7x-3y\] |
| \[\Rightarrow \] \[9x-7x=4y-3y\] |
| \[\Rightarrow \] \[2x=y\] (iii) |
| From Eq. (i), |
| \[9x-4y=200\] |
| \[\Rightarrow \] \[9x-8x=200\] |
| \[\therefore \] \[x=200\] |
| \[\therefore \]Sum of their weekly incomes \[=16x=16\times 200\] |
| \[=\text{Rs}\text{.}\,\,\text{3200}\] |
| Alternate Method |
| Let A's income \[=\text{Rs}\text{.}\,\,9x\] |
| B's income \[=\text{Rs}\text{.}\,\,7x\] |
| According to the question, |
| \[\frac{9x-200}{7x-200}=\frac{4}{3}\] |
| \[\Rightarrow \] \[27x-600=28x-800\] |
| \[\Rightarrow \] \[x=200\] |
| A's income \[=9\times 200=\text{Rs}\text{. 1800}\] |
| and B's income \[=7\times 200=\text{Rs}\text{. 1400}\] |
| Sum \[=1400+1800=\text{Rs}\text{. 3200}\] |
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