Question

the number whose sum is 180 are in the ration of 3:2 the larger number is​

Answer 1

Step-by-step explanation:

Let the numbers be x, y and z then its given that x+y+z=180

y

x

=

z

1

⇒y=2xx+y+z=180

⇒y=2x and z=180−y−x

=180−2x−x

=180−3x

Let P denote product of the numbers

Then P=xyz

P=x×2x×(180−3x)

=2x

2

(180−3x)

P=360x

2

−6x

3

dx

dP

=720x−18x

2

dx

2

d

2

P

=720−36x

For maximum or minimum value of P

we must have

dx

dP

=0

⇒720x−18x

2

=0

x=40

(

dx

2

d

2

P

)

x=40

=720−360×40<0

Hence P is maximum when x=40

Now, x=40 y=2x=2×=80 z=180−3x=180−3×40=180−120=60.

Numbers are 40,80 and 60.

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