Question
By interchanging the digits of a two digit number we get a number which is four times the original number minus 24. If the unit’s digit of the original number exceeds its ten’s digit by 7, then original number is
Answer: Option B
Answer: (b)Let the two–digit number be 10x + y where x < y. Number obtained on reversing the digits =10y + x According to the question, 10y + x = 4 (10x + y) – 2440x + 4y – 10y – x = 2439x – 6y = 2413x – 2y = 8 ....(i) Again, y – x = 7y = x + 7 ....(ii) 13x – 2 (x + 7) = 813x – 2x – 14 = 811 x = 14 + 8 = 22x = $22/11$ = 2From equation (ii), y – 2 = 7 ⇒ y = 2 + 7 = 9Number = 10x + y =10×2+9= 29
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Answer: (b)Let the two–digit number be 10x + y where x < y. Number obtained on reversing the digits =10y + x According to the question, 10y + x = 4 (10x + y) – 2440x + 4y – 10y – x = 2439x – 6y = 2413x – 2y = 8 ....(i) Again, y – x = 7y = x + 7 ....(ii) 13x – 2 (x + 7) = 813x – 2x – 14 = 811 x = 14 + 8 = 22x = $22/11$ = 2From equation (ii), y – 2 = 7 ⇒ y = 2 + 7 = 9Number = 10x + y =10×2+9= 29
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