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:
Option 1: 48
Option 2: 64
Option 3: 46
Option 4: 36
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.
Option 1: 81
Option 2: 18
Option 3: 62
Option 4: 26
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?
Option 1: 62
Option 2: 34
Option 3: 26
Option 4: 43
Question : Directions: By interchanging the given two signs which of the following equations will be correct? × and +
Option 1: 7 × 8 ÷ 9 + 18 – 11 = 16
Option 2: 24 – 8 – 5 × 5 + 3 = 14
Option 3: 5 × 10 – 15 + 20 ÷ 25 = 8
Option 4: 24 × 8 + 6 ÷ 3 – 18 = 22
Question : Directions: Select the correct combination of mathematical signs to sequentially replace the % signs and to balance the given equation. [{(32 % 28) % (6 % 4)} % (1 % 7)] % 5 % 20
Option 1: −, +, ×, ÷, ×, ×, =
Option 2: ×, ÷, ×, ×, −, +, =
Option 3: ×, −, +, ×, ÷, ×, =
Option 4: −, +, ×, ×, ×, ×, =
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