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  • Question
  • In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:


  • Options
  • A. 24
  • B. 26
  • C. 42
  • D. 46

  • Correct Answer
  • 24 

    Explanation
    Let the ten's digit be x.

    Then, unit's digit = x + 2.

    Number = 10x + (x + 2) = 11x + 2.

    Sum of digits = x + (x + 2) = 2x + 2.

    ∴ (11x + 2)(2x + 2) = 144

    ⟹ 22x2 + 26x - 140 = 0

    ⟹ 11x2 + 13x - 70 = 0

    ⟹ (x - 2)(11x + 35) = 0

    x = 2.

    Hence, required number = 11x + 2 = 24.


    Problems on Numbers


    Search Results


    • 1. The sum of two number is 25 and their difference is 13. Find their product.

    • Options
    • A. 104
    • B. 114
    • C. 315
    • D. 325
    • Discuss
    • 2. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

    • Options
    • A. 564
    • B. 645
    • C. 735
    • D. 756
    • E. None of these
    • Discuss
    • 3. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

    • Options
    • A. 40
    • B. 400
    • C. 5040
    • D. 2520
    • Discuss
    • 4. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

    • Options
    • A. 10080
    • B. 4989600
    • C. 120960
    • D. None of these
    • Discuss
    • 5. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

    • Options
    • A. 159
    • B. 194
    • C. 205
    • D. 209
    • E. None of these
    • Discuss
    • 6. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

    • Options
    • A. 145
    • B. 253
    • C. 370
    • D. 352
    • Discuss
    • 7. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

    • Options
    • A. 3
    • B. 5
    • C. 9
    • D. 11
    • Discuss
    • 8. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

    • Options
    • A. 18
    • B. 24
    • C. 42
    • D. 81
    • Discuss
    • 9. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

    • Options
    • A. 380
    • B. 395
    • C. 400
    • D. 425
    • Discuss
    • 10. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

    • Options
    • A. 3
    • B. 4
    • C. 9
    • D. Cannot be determined
    • E. None of these
    • Discuss


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