PYQ
Base āĻāĻā§ (>1) āĻš'āϞ⧠āĻā§ā§ąāϞ Exponent āϤā§āϞāύāĻž āĻā§°āĻ → āϝāĻžā§° Exponent āĻĄāĻžāĻā§°, āϏā§āĻ āϏāĻāĻā§āϝāĻžāĻ āĻĄāĻžāĻā§°āĨ¤
āĻāĻĻāĻžāĻšā§°āĻŖ:
āϝāĻŋāĻšā§āϤ⧠9 > 6, āϏā§āϝāĻŧā§
āĻŽāύāϤ ā§°āĻžāĻāĻŋāĻŦ: Base āĻāĻā§ → Exponent āϤā§āϞāύāĻž āĻā§°āĻ → āĻĄāĻžāĻā§° Exponent = āĻĄāĻžāĻā§° āϏāĻāĻā§āϝāĻžāĨ¤
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Q. If the sum of the digits of a two-digit number is 9 and adding 27 to it reverses its digits, find the unit digit of the number.(āĻāĻāĻž āĻĻā§āĻāĻž āĻ āĻāĻā§° āϏāĻāĻā§āϝāĻžā§° āĻ āĻāĻ āĻĻā§āĻāĻžā§° āϝā§āĻāĻĢāϞ ⧝āĨ¤ āϏā§āĻ āϏāĻāĻā§āϝāĻžāϤ ⧍⧠āϝā§āĻ āĻā§°āĻŋāϞ⧠āĻ āĻāĻ āĻĻā§āĻāĻž āĻāϞā§āĻāĻž āĻšā§ āϝāĻžāϝāĻŧāĨ¤ āϏāĻāĻā§āϝāĻžāĻā§ā§° āĻāĻāĻ āĻ āĻāĻ āύāĻŋā§°ā§āĻŖāϝāĻŧ āĻā§°āĻāĨ¤)
A. 4 B. 6 C. 3 D. 5
Trick | āĻā§ā§°āĻŋāĻ
Try the options where the sum of the digits is 9. (āϝāĻŋāĻŦā§ā§° āϏāĻāĻā§āϝāĻžā§° āĻ āĻāĻ āĻĻā§āĻāĻžā§° āϝā§āĻāĻĢāϞ ⧝ āĻšāϝāĻŧ, āϏā§āĻāĻŦā§ā§° āĻĒā§°ā§āĻā§āώāĻž āĻā§°āĻāĨ¤)
- 36 + 27 = 63 (Digits are reversed.)
- 45 + 27 = 72
- 54 + 27 = 81
- 63 + 27 = 90
Therefore, the original number is 36. (āϏā§āϝāĻŧā§, āĻŽā§āϞ āϏāĻāĻā§āϝāĻžāĻā§ āĻšā§āĻā§ 36āĨ¤)
Ans | āĻāϤā§āϤ⧰ : Unit digit = 6 | āĻāĻāĻ āĻ āĻāĻ = 6
Ans: B. 6