Question

The sum of the LCM and HCF of two numbers is 176 and their difference is 160. Difference between the numbers is 32.

To find :
Determine the sum of the  numbers.

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Answer 1

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named as Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

Answer 2

Given :

The sum of the LCM and HCF of two numbers is 176 and their difference is 160. Difference between the numbers is 32.

To find :

Determine the sum of the  numbers.

Solution :

LCM + HCF = 176 (1)

LCM - HCF = 160 (2)

Now adding both equations :

⇒ LCM + HCF + LCM - HCF = 176 + 160

⇒ 2LCM = 336

⇒ LCM = 336/2

⇒ LCM = 168

Now putting this value in (1) :

⇒ 168 + HCF = 176

⇒ HCF = 176 - 168

⇒ HCF = 8

Now we know,

HCF × LCM = Product of 2 numbers.

Now, difference b/w numbers = 32

Let the numbers be 'a' and 'b'     [Where, a > b]

⇒ a - b = 32

⇒ a = b + 32

Now,

⇒ HCF × LCM = ab

⇒ 168 × 8 = (b + 32)b

⇒ b² + 32b = 1344

⇒ b² + 32b - 1344 = 0

⇒ b² + 56b - 24b - 1344 = 0

⇒ b(b + 56) - 24(b + 56) = 0

⇒ (b - 24)(b + 56) = 0

⇒ b = 24   or,   b = - 56

∵ We will neglect negative values here.

∴ b = 24

Now putting value,

⇒ a = 24 + 32

⇒ a = 56

∴ Sum of the numbers = a + b

                                      = 56 + 24

                                      = 80

∴ Sum of the numbers = 80