Question

two numbers a and b are such that 3a-4b=0 and their lcm is 120. then the sum of the numbers is​

Answer 1

Step-by-step explanation:

Given :-

Two numbers a and b are such that 3a-4b=0.

Their LCM is 120.

To find :-

The sum of the numbers.

Solution :-

Given that

The two numbers = a and b

Given relation between a and b

= 3a-4b = 0

=> 3a = 4b

=> a / b = 4/3

=> a:b = 4:3

Let they be 4X and 3X

Let a = 4X

Let b = 3X

LCM of a and b = 4×3×X

LCM of a and b = 12X

According to the given problem

LCM of a and b = 120

=> 12X = 120

=> X = 120/12

=> X = 10

Therefore, The value of X = 10

Now,

If X = 10 then 4X = 4(10) = 40

If X = 10 then 3X = 3(10) = 30

Therefore, a = 40 and b = 30

The sum of the two numbers

a+b = 40+30 = 70

Answer:-

The sum of the two numbers is 70

Check :-

a = 40

b = 30

Their LCM = 4×3×10 = 120

and 3a-4b

= 3(40)-4(30)

= 120-120

3a-4b = 0

Verified the given relations in the given problem.

Answer 2

Step-by-step explanation:

Step-by-step explanation:

Given :-

Two numbers a and b are such that 3a-4b=0.

Their LCM is 120.

To find :-

The sum of the numbers.

Solution :-

Given that

The two numbers = a and b

Given relation between a and b

= 3a-4b = 0

=> 3a = 4b

=> a / b = 4/3

=> a:b = 4:3

Let they be 4X and 3X

Let a = 4X

Let b = 3X

LCM of a and b = 4×3×X

LCM of a and b = 12X

According to the given problem

LCM of a and b = 120

=> 12X = 120

=> X = 120/12

=> X = 10

Therefore, The value of X = 10

Now,

If X = 10 then 4X = 4(10) = 40

If X = 10 then 3X = 3(10) = 30

Therefore, a = 40 and b = 30

The sum of the two numbers

a+b = 40+30 = 70

Answer:-

The sum of the two numbers is 70

Check :-

a = 40

b = 30

Their LCM = 4×3×10 = 120

and 3a-4b

= 3(40)-4(30)

= 120-120

3a-4b = 0

Verified the given relations in the given problem.

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