Question

The sum of three numbers is 123. If the ratio between first and second number is 2:5 and that of between second and third is 3:4 then find the difference between second and third number.

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Answer 1

Answer:

Ratio of 1 st and 2 nd number = 2:5 = 6:15

Ratio of 2 nd and 3 rd number = 3:4 = 15:20

Hence the ratio of three numbers is 6:15:20

Hence the numbers are 6x , 15x , 20x

Sum of numbers = 6x + 15x + 20x = 123

41x = 123

x = 3

Hence the numbers are 6*3 , 15*3 , 20*3

= 18 , 45 , 60

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Answer 2

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Let the three numbers be a, b, and c.

--› Given :-

Ist Condition

• a:b = 2:5 => a:b=6:15

2nd Condition

• b:c = 3:4 =>b:c = 15:20

>>>From Above equation

• a:b:c = 6:15:20

Let take

a = 6x, b = 15x and c = 20x

Given

Sum of three number = 123

Lets Adding the three numbers

a+b+c =123

=> 6x+15x+20x =123

=> 41x = 123

We get

$\pink{\large{\boxed{ => x = 3}}}$

Hence a = 18, b = 45 and c = 60.

The difference between the second and the third number is

$\Large{\purple{\boxed{\implies{\rm{60 - 45 = 15}}}}}$

a = 18×3=54, b = 45×3=135 and

c=60×3=180

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