# Problems on Numbers

## Problems on Numbers

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 Question 1
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
 A 35 B 36 C 45 D 54
Question 1 Explanation:
Let the number be x. hen, (1/3)of (1/4) of x = 15 x = 15 x 12 = 180. So, required number =(3/10)x 180= 54.
 Question 2
Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:
 A 9 B 11 C 13 D 15
Question 2 Explanation:
Let the three integers be x, x + 2 and x + 4. Then, 3x = 2(x + 4) + 3 ==> x = 11. Third integer = x + 4 = 15.
 Question 3
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?
 A 3 B 4 C 9 D 11
Question 3 Explanation:
Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (10y + x) = 36 9(x - y) = 36 x - y = 4.
 Question 4
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
 A 4 B 8 C 16 D 32
Question 4 Explanation:
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit. Let ten's and unit's digits be 2x and x respectively. Then, (10 x 2x + x) - (10x + 2x) = 36 9x = 36 x = 4. Required difference = (2x + x) - (2x - x) = 2x = 8.
 Question 5
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?
 A 69 B 78 C 96 D None of these
Question 5 Explanation:
Let the ten's digit be x and unit's digit be y. Then, x + y = 15 and x - y = 3 or y - x = 3. Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6. Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9. So, the number is either 96 or 69. Hence, the number cannot be determined.
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