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If we divide the unknown 2-digit number by the number consisting of the same numbers in reverse order, we get 2 as quotient and 10 as a remainder. If we divide the required number by the sum of its digits, we get 7 as quotient and 6 as a remainder. Find the number.

If we divide the unknown 2-digit number by the number consisting of the same numbers in reverse order, we get 2 as quotient and 10 as a remainder. If we divide the required number by the sum of its digits, we get 7 as quotient and 6 as a remainder. Find the number. Correct Answer 62

Let the required 2-digit number be (10x+y), sum of its digits be (x+y) and reverse of the number be (10y+x). By data, (10x + y) = 2(10y + x) + 10 i.e., 8x – 19y = 10 …… (i) Also, (10x + y) = 7(x + y) + 6 i.e., x – 2y = 2 …… (ii) Solving (i) and (ii), we get, x = 6 and y = 2 Hence, the required number is 62.

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