EX 11. The ratio between a two – digit number and the sum of the
digits of that number is 4:1. If the digit in the unit’s place is 3 more than
the digit in the ten’s place what is the number?
Sol. let the ten’s digit be x. then, unit’s digit = (X + 3).
Sum of the digits = X + (X + 3) = 2X + 3. Number = 10x + (X + 3) =
11x + 3.
11X + 3 / 2x + 3 = 4/1
11X + 3 = 4 (2X + 3) 3X + 9 X = 3.
Hence, required number = 11X + 3 = 36.
Ex. 12. A number consists of two digits. The sum of the digits is
9. If 63 is subtracted from the number, its digits are interchanged. Find the
number.
Sol. let the ten’s digit be. Then, unit’s digit = (9 –X).
Number = 10X + (9-x) = 9X + 9.
Number obtained by reversing the digits = 10 (9-x) + = 90 – 9x.
(9X + 9) – 63 = 90 – 9X 18X
= 144 X = 8.
So, ten’s digit = 8 and unit’s digit = 1.
Hence, the required number is 81.
Ex. 13. A fraction becomes 2/3 when 1 is added to both, its
numerator and denominator. Ned, it becomes ½ when 1 is subtracted from both the
numerator and denominator. Find the fraction.
