Problems on Numbers with Explanation

Q15. Five by eight of a first number is equal to one-fifth of another number. Four times of the first number exceeds the second number by 35. The second number is?

Answer- Option A

Explanation-

Let first number be x.
Then, second number is (4x - 35)
According to the question,

5x 8

=

1 5

(4x - 35)

25x = 32x - 280
7x = 280
x = 40
The second number is (4x - 35) = 125

Q16. A two-digit number is such that the unit's place digit is double the digit in the ten's place. The number exceeds the sum of its own digits by 27. The number is:

Answer- Option B

Explanation-

Let the ten's digit be x. Then, unit's digit = 2x
Original Number = 10x + 2x = 12x
12 = x + 2x + 27
9x = 27
x = 3
So, ten's digit = 3 and unit's digit = 6
Hence, the number is 36

Q17. In a two-digit number, the difference between its unit's digit and ten's digit is 2. The product of the given number and the sum of its digits is equal to 144. What is that two-digit number?

Answer- Option C

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
11x² + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, the number is 24

Q18. There is a two-digit number such that, unit's place digit exceeds twice the digit at ten's place by 1. If the digits in the ten's place and unit's place are interchanged, a difference between the newly obtained number and the original number is less than the original number by 1. Find the original number?

Answer- Option A

Explanation-

Let the ten's digit be x. Then, unit's digit = 2x + 1
Original Number = 10x + (2x + 1) = 12x + 1
Newly formed number = 10(2x + 1) + x = 21x + 10
(21x + 10) - (12x + 1) = (12x + 1) - 1
3x = 15
x = 5
So, ten's digit = 5 and unit's digit = 7
Hence, the number is 37