Question : By interchanging the digits of a two-digit number, we get a number that 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 the original number is:
Option 1: 29
Option 2: 36
Option 3: 58
Option 4: 18
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Correct Answer: 29
Solution : Let the original number be (10P + Q) and its reversed number be (10Q + P). By interchanging the digits of a two-digit number, we get a number that is four times the original number minus 24. (10Q + P) = 4 × (10P + Q) – 24 ⇒ 39P – 6Q = 24 ⇒ 13P – 2Q = 8 .....................(i) Again, Q – P = 7 ....................(ii) Solving equation (i) and equation (ii), We get, P = 2 and Q = 9 The original number is 10P + Q = 10 × 2 + 9 = 29 Hence, the correct answer is 29.
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Question : In a two-digit number, its unit digit exceeds its tens digit by 2 and the product of the given number and the sum of its digits is equal to 460. The number is:
Question : The tens digit of a two-digit number is larger than the unit digit by 7. If we subtract 63 from the number, the new number obtained is a number formed by the interchange of the digits. Find the number.
Question : The product of the digits of a 2-digit number is 12. If we add 36 to the number, the new number obtained is a number formed by the interchange of the digits. What is the number?
Question : Directions: By interchanging the given two signs which of the following equations will be correct? × and +
Question : Directions: By interchanging the given two signs which of the following equations will be not correct? + and ÷
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