Two numbers are in the ratio 2:3. If the larger number is 30 more than half of the smaller, find the
numbers.
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Answered by
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Step-by-step explanation:
Let the two numbers be x and y such that y > x
Since, they mentioned that the larger number is 30 more than the half of the smaller number, we xan write is as ;
y = 30 + x/2 ➡️ eq (1)
And. x : y = 2 : 3. ( As given in the question )
By cross multiplication,
We get x = 2/3 (y)
And x/2 =y/3
So, now let's substitute the value of x in eq (1)
So, we get
y = 30 + y/3
(y) - (y/3) = 30
So by taking L.C.M in the L.H.S part, we get
(3y - y)/ 3= 30
2y= 30×3 = 90
And. y= 45
And as we know ,
x = 2/3(y) = 2/3 (45) = 30
So the two numbers are 30 and 45
Hope it helps !
Answered by
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Let us consider the two numbers to be x and y So, x:y=2:3 3x=2y And, y- (x/2)=30 2y-x=60 3x-x=60 2x=60 x= 30 So, y=45
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