Question

Ratio between two numbers is 3:4 and their sum is 420,.Ffind smaller number

Answer 1

let the numbers be a,b
a/b=3/4
applying componendo and dividendo
a+b/a-b=3+4/3-4
420/a-b=7/1
a-b=60
a+b=420
2a=480
a=240
b=180

Answer 2

Given that the ratio between two numbers = 3 : 4

let the constant ratio be ' x '

since the mumbers have a constant ratio then
definitely there will be a common multiple of 3 and 4 .

let the numbers are 3x , 4x

here x will be that required common multiple of 3 and 4 .
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according to question,

sum of these two numbers = 420

3x + 4x = 420

7x = 420

x = 60

smallest number = 3x = 3 × 60 = 180

therefore , smallest number = 180
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Your answer = 180
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in addition :
greatest number =4x = 4 × 60 = 240
thus , those two numbers are 180 and 240 whose sum = 420
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