Problems on Numbers

Correct answer.
Let the number = x
Then, 1/3 of 1/4 of of x = 15
x = 15 x 12
x = 180
So, the required number = (3/10) * 180 = 54

Let the ten's and unit digit be x and 8/x, respectively.
Then, (10x + 8/x) + 18 = 10 x (8/x) + x
10x² + 8 + 18x = 80 + x²
9x² + 18x - 72 = 0
x² + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2.
So, unit's digit = 4 and ten's digit = 2
Then, the required number is 24.
Therefore, the correct answer is 24.

Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3
x = 11.
Third integer = x + 4 = 15.
Therefore, 15 is correct answer.

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 the ten's and the 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
Therefore, 8 is the correct answer.

Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400
(a + b + c) = 20

Let the middle digit be b.
Then, 2b = 10 or b = 5.
Let the number be abc.
Now, 100 a + 10 b + c + 99 = 100 c + 10 b + a
Or, a + 1 = c
So, the number is  253

Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x + y)² - (x- y)²
4xy = (25)² - (13)²
4xy = (625 - 169) = 456
xy = 114

Then, (x + 2)² - x² = 84 4x + 4 = 84  4x = 80  x = 20  The required sum = x + (x + 2) = 2x + 2 = 42

Let the ten's digit be x.
Then, unit's digit will be x + 2.
The number = 10x + (x + 2) = 11x + 2
The 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, the required number = 11x + 2 = 24

Let the numbers be x and y.
Then, xy = 9375 and x/y = 15
(xy)/(x/y) = 9375/15
y2 = 625
y = 25
x = 15y
= (15 x 25) = 375
Sum of the numbers = x + y = 375 + 25 = 400.

Then, x + 17 = 60/x x² + 17x - 60 = 0  (x + 20)(x - 3) = 0  x = 3

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, out of the given options, option (1) is correct.
 

Let the ten's digit be x and the unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4

Let the ten's digit be x and the unit's digit be y. Then, the number = 10x + y.
The number obtained by interchanging the digits = 10y + x
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

Then, xy = 120 and x² + y² = 289.  (x + y)² = x² + y² + 2xy               = 289 + (2 x 120)               = 529  x + y  = 23