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?
Answers
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:
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,
5x = 3y
x = -------------------------(2)
Since the ratio of the second number to the third number 2:3, we have
3y = 2z
z = ----------------------(3)
Substituting the values of x and z in equation (1) we get
× y × = 900
= 900
9y³ = 9000
y³ = 1000
y = ∛1000 = 10
∴The second number = y = 10
The first number = x = = ×10 = 6
The third number = z = = ×10 = 15
∴ The difference between y and z = 15 -10 = 5
The difference between the second and third number = 5
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