Eight times a two digit number is equal to three times the number reversing
Answers
Let the digit in the ones place be y and tens place be x Therefore the number = 10x + y Number formed by reversing the digits = 10y + x Given 8(10x + y) = 3(10y + x) ⇒ 80x + 8y = 30y + 3x ⇒ 77x – 22y = 0 ∴ 7x – 2y = 0 → (1) It is also given that the difference between the digits is 5. Hence (y – x) = 5 – x + y = 5 → (2) Multiply equation(2) with 2 and add to equation (1), we get 7x – 2y = 0 –2x + 2y = 10 ---------------- 5x = 10 ∴ x = 2 Put x = 2 in – x + y = 5, we get – 2 + y = 5 ⇒ y = 7 Hence the number = (10x + y) = (10×2 + 7) = 27
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➡️ 10x + y.
➡️ Reversed = 10y + x.
▪️By condition,
8(10x + y) = 3(10y + x)
Or, 80x + 8y = 30y + 3x.
Or, 77x = 22y.
Or, 7x = 2y.
Or, x = 2y/7.
▪️Again, it is given that the difference between them is 5.
So,
y - x = 5.
Or, y - 2y/7 = 5.
Or, 5y/7 = 5.
Or, y = 7.
▪️And,
x = 7 - 5 = 2.
✨ Hence, the number is
= 2 * 10 + 7.
= 27.
That's it..