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Two-digit number and its reverse (10a + b, 10b + a): find the number or its digits

This type of question, asked 9 times: CDS 1 2018, CDS 2 2020, CDS 2 2021, CDS 2 2022, CDS 1 2023, CDS 2 2023, CDS 2 2025, CDS 1 2026, CDS 2 2026. All 9 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2018

    39
    The age of a woman is a two-digit integer. On reversing this integer, the new integer is the age of her husband who is elder to her. The difference between their ages is one-eleventh of their sum. What is the difference between their ages?

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  2. Question 2

    CDS 2 2020

    36
    The sum of the digits of a two digit number is 13 and the difference between the number and that formed by reversing the digits is 27. What is the product of the digits of the number ?

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  3. Question 3

    CDS 2 2021

    32
    A two-digit number is such that the product of the digits is 8. If 63 is added to this number, the digits interchange their places. What is the sum of the digits in the number ?

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  4. Question 4

    CDS 2 2022

    27
    Consider the question and two statements given below : A 2-digit number is added to the number formed by reversing the digits of the 2-digit number. Question : What is the 2-digit number ? Statement-1 : The sum is divisible by 9. Statement-2 : The sum is divisible by 2. Which one of the following is correct in respect of the question and the statements ?

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  5. Question 5

    CDS 1 2023

    9
    The sum of digits of a 2-digit number is 12. When the digits are reversed, the number becomes greater by eighteen. What is the difference between the digits in the number?

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  6. Question 6

    CDS 2 2023

    3
    A 2-digit number is such that the sum of the number and the number obtained by reversing the order of the digits of the number is 55. Further, the difference of the given number and the number obtained by reversing the order of the digits of the number is 45. What is the product of the digits ?

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  7. Question 7

    CDS 2 2025

    82
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : The product of a natural number NN and the number MM written by the same digits of NN in the reverse order is 252. What is the number NN? Statement-I : N+M=33N + M = 33 Statement-II : N>MN > M Which one of the following is correct in respect of the above Question and the Statements?

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  8. Question 8

    CDS 1 2026

    11
    Seven times a two-digit positive number is equal to four times the number obtained by reversing the order of the digits. How many such two-digit numbers are there ?

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  9. Question 9

    CDS 2 2026

    23
    A number N consists of two digits. The digit in the tens place is 3 times the digit in the units place. The digits are reversed and the resulting number is denoted by R. If N×R=3627N \times R = 3627, then what is the product of the digits of the number N ?

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