Find the digits A and B, if : A B + 3 7 = 9 A

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KnowledgeBoat · Accepted Answer

Lets take A as a 1-digit number B + 7 = A .....(1) A + 3 = 9 .....(2) A = 9 - 3 = 6 Putting the value of A in equation (1), we get B + 7 = 6 B = 6 - 7 B = -1 ∴ As we know B is a digit. Hence B ≠ -1. Lets take A as a 2-digit number with ones digit as 1. We can represent A as 10 + A B + 7 = 10 + A .....(3) 1 + A + 3 = 9 (one carry on ten's digit) .....(4) A + 4 = 9 A = 9 - 4 = 5 Putting the value of A in equation 3. B + 7 = 10 + 5 B + 7 = 15 B = 15 - 7 = 8 Hence, A = 5, B = 8 Now, lets take A as a 2-digit number with ones digit as 2. We can represent A as 20 + A B + 7 = 20 + A .....(5) 2 + A + 3 = 9 (two carry on ten's digit) .....(6) A + 5 = 9 A = 9 - 5 = 4 Putting the value of A in equation (5), B + 7 = 20 + 4 B + 7 = 24 B = 24 - 7 = 17 ∴ As we know B is a digit. Hence B ≠ 17. Hence, A = 5 , B = 8.

Mathematics

Find the digits A and B, if : A B + 3 7 = 9 A

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