Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.
Solution:
Given, three numbers are in the ratio 2 : 3 : 4
The sum of their cubes is 0.334125.
We have to find the numbers.
Let the numbers be 2x, 3x and 4x.
According to the question,
(2x)³ + (3x)³ + (4x)³ = 0.334125
8x³ + 27x³ + 64x³ = 0.334125
99x³ = 0.334125
x³ = 0.334125/99
x³ = 0.003375
Taking cube root,
∛x³ = ∛0.003375
= ∛3375/1000000
By using long division,
3375 = 3 × 3 × 3 × 5 × 5 × 5
∛3375 = ∛(15)³
= 15
1000000 = 10 × 10 × 10 × 10 × 10 × 10
∛1000000 = 10 × 10 × 10
= 1000
So, x = 15/1000 = 0.015
Now, 2x = 2(0.015) = 0.030
3x = 3(0.015) = 0.045
4x = 4(0.015) = 0.060
Therefore, the required numbers are 0.03, 0.045 and 0.06.
✦ Try This: Three numbers are in the ratio 1:3:5. The sum of their cubes is 1224. Find the numbers.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 134
Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers
Summary:
Three numbers are in the ratio 2:3:4 and the sum of their cubes is 0.334125. The numbers are 0.03, 0.045 and 0.06.
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