Question

Product of three positive numbers is 900.. If the ratio of the first number to the second number is 3:5 and that of the second number to the third number is 2:3, what is the difference between the second and the third numbers?​

Answer 1

Step-by-step explanation:

Product =900

Ratio of first and second =3:5

Ratio of second and third =2:3

Now

• 3 : 5 : : 2 : 3 = 900
• 3x / 5x × 2x/3x =900
• 2/5x =900
• X=2250

Now,

• 3x=3 ×2250
• =6750
• 5x= 5 ×2250
• =12250
• 2x=2 × 2250
• =4500

Since 3 is in both ratio therefore we can say that 3x is second no. And also 5x is first no. And 2x is third no.

Difference =second-third

• 3x-2x
• 6750-4500
• =2250 answer

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Answer 2

Answer:

The difference between the second and third number  = 5

Step-by-step explanation:

Given,

The product of three positive numbers = 900

The ratio of the first number to the second number is 3:5

The second number to the third number is 2:3

To find,

The difference between the second and third number

Solution

Let x, y, z be the first second, and third numbers respectively.

Since the product of the numbers  = 900, we have

x×y×z = 900 -------------------(1)

Since the ratio of the first number to the second number is 3:5 we have,

$\frac{x}{y} = \frac{3}{5}$

5x = 3y

x = $\frac{3}{5} y$ -------------------------(2)

Since the ratio of the second number to the third number 2:3, we have

$\frac{y}{z} = \frac{2}{3}$

3y = 2z

z = $\frac{3}{2} y$ ----------------------(3)

Substituting the values of x and z in equation (1) we get

$\frac{3}{5} y$ × y × $\frac{3}{2} y$ = 900

$\frac{9y^3}{10}$ = 900

9y³ = 9000

y³  = 1000

y = ∛1000 = 10

∴The second number = y = 10

The first number  = x =  $\frac{3}{5} y$ = $\frac{3}{5}$ ×10 = 6

The third number = z =  $\frac{3}{2} y$  = $\frac{3}{2}$ ×10 = 15

∴ The difference between y and z  = 15 -10 = 5

The difference between the second and third number  = 5

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