| The incomes of A, B and C are in the ratio 7: 9: 12 and their spendings are in the ratio 8: 9: 15. If A saves \[\frac{1}{4}th\] of his income, then the savings of A, B and C are in the ratio of |
A) 69: 56: 48
B) 47: 74: 99
C) 37: 72: 49
D) 56: 99: 69
Correct Answer: D
Solution :
| Let incomes of A, B and C are Rs. 7x, Rs. 9x and Rs. 12x and their expenses are Rs. 8y, Rs. 9y and Rs. 15y. |
| \[\therefore \] \[7x-8y=\frac{7x}{4}\,\,\,\Rightarrow \,\,\,7x\times \frac{3}{4}=8y\] |
| \[\Rightarrow \] \[x=\frac{8\times 4}{7\times 3}y=\frac{32}{21}y\,\,\,\Rightarrow \,\,\,y=\frac{21x}{32}\] |
| \[\therefore \] Saving of \[B=9x-9y=9x-9\times \frac{21}{32}x=\frac{99}{32}x\] |
| and saving of \[C=12x-15y\] |
| \[=12x-15\times \frac{21}{32}x=Rs.\frac{69}{32}x\] |
| Hence, required ratio \[=\frac{7}{4}x:\frac{99}{32}x:\frac{69}{32}x\] |
| \[=56:99:69\] |
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