In a two-digit number, the sum of digits is (11). On reversing the digits, the number decreases by (27). What is the original number?
Answer and explanation
Correct answer: 74
Let the tens digit be x and the units digit be y. Then x + y = 11. The original number is 10x + y, while the reversed number is 10y + x. Since the number decreases by 27 on reversal, (10x + y) − (10y + x) = 27, giving 9(x − y) = 27 and hence x − y = 3. Solving x + y = 11 and x − y = 3 gives x = 7 and y = 4. Therefore, the original number is 74. Option 83 has a digit sum of 11, but reversing it causes a decrease of 45, not 27. Exam tip: Represent a two-digit number as 10x + y before forming the equations.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
Let the tens digit be x and the units digit be y. Then x + y = 11. The original number is 10x + y, while the reversed number is 10y + x. Since the number decreases by 27 on reversal, (10x + y) − (10y + x) = 27, giving 9(x − y) = 27 and hence x − y = 3. Solving x + y = 11 and x − y = 3 gives x = 7 and y = 4. Therefore, the original number is 74. Option 83 has a digit sum of 11, but reversing it causes a decrease of 45, not 27. Exam tip: Represent a two-digit number as 10x + y before forming the equations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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