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The ten's digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is 32. Find the number.

(ii) The annual incomes of A and B are in the ratio 3:4 and their annual expenditures are in the ratio 5:7. If each saves Rs. 5,000; find their annual incomes.


Let the ten's digit be y and unit digit be x. Then the required number is 10y+x.
Given the ten's digit is three times the unit digit. So y=3x.
Also given that the sum of the number and the unit digit is 32 which means 10y+x+x=32. Substituting the value of y=3x in this equation we get 10(3x)+x+x=32. i.e 30x+2x=32 ie 32x=32 from which we get x=1.
Now substituting the value of x in y=3x, we get y=3. Thus the required answer is 31.
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