A) 56 : 99 : 69
B) 99 : 56 : 69
C) 69 : 56 : 99
D) 99 : 69 : 56
Correct Answer: A
Solution :
| [a] Let the income of A, B and C is Rs. 7x, Rs. 9x and Rs. 12x and their expenditure is Rs. 8y, Rs. 9y and Rs. 15y respectively. According to the question, Saving of A, \[\Rightarrow \]\[7x-8y=\frac{7x}{4}\] (i) \[\Rightarrow \] \[28x-32y=7x;\] \[21x=32y\] \[\therefore \] \[y=\frac{21x}{32}\] Saving of B, \[\Rightarrow \]\[9x-9y\] \[=9x-9\times \left( \frac{21x}{32} \right)\] (Putting the value of y) \[=\frac{32\times 9x-9\times 21x}{32}\] \[\Rightarrow \] \[9x-9y=\frac{99x}{32}\] (ii) Also, saving of C \[\Rightarrow \]\[12x-15y\] \[=12x-15\times \left( \frac{21x}{32} \right)\] (Putting the value of y) \[=\frac{32\times 12x-15\times 21x}{32}=\frac{69x}{32}\] (iii) Therefore ratio of their savings \[=\frac{7x}{4};\,\,\frac{99x}{32};\,\,\frac{69x}{32}\] [by Eqs. (i), (ii), (iii)] \[=56:99:69\] |
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