Question

Sum of two consecutive multiples of a number is 120. Find these multiples

Answer 1

answer

-1+root of 479/2 or -1-root of 479/2

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Answer 2

Concept

Consecutive multiples are the factors that multiply upto a certain number but are in order. For example 28, 35, 42  are consecutive multiples of 7

Given

Sum of two consecutive multiples of a number is 120.

Solution

Let the number be y and the first multiple be my and the second multiple will be (m+1)y

my+(m+1)y = 120

y(2m+1) = 120

y = 120/(2m+1)

As (2m+1) is an odd number which means our number y is 120 divided by an odd number.

Factorizing 120 = 2 * 2 *2 * 3 * 5

So the factors we can get for 120 are 3, 5

Case 1

When Odd factor is 3

y =120/3

y = 40

2m+1=120/y

2m+1 = 3

m=1

So the required number is 40 and the multiples are 40, 80 ( 1*40, 2*40)

Case 2

When Odd factor is 5

y = 120/5

y=24

2m+1 = 120/y

2m+1 = 120/24

2m+1 = 5

m=2

So the required number is 24 and the multiples are 48, 72 ( 2*24, 3*24)

 

So the number y  is either 40( multiplied to 1 and 2) or 24(multiplied to 2 and 3) to get the sum of 120.

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