Question

Three numbers are in the ratio of 1 : 3 : 5. If sum of cubes of these numbers is 1224. Find the numbers.

Answer 1

Gɪᴠᴇɴ :-

• Ratio of three numbers = 1:3:5
• Sum of cubes = 1224

ᴛᴏ ғɪɴᴅ :-

• Three numbers

sᴏʟᴜᴛɪᴏɴ :-

Let the ratio of numbers be 1x : 3x : 5x

then,

➢ According to Question :-

➭ (1x) ³ + (3x) ³ + (5x) ³ = 1224

➭ x³ + 27x³ + 125x³ = 1224

➭ 153x³ = 1224

➭ x³ = 1224/153

➭ x³ = 8

➭ x = ³√8

➭ x = 2

Hence,

• First number = x = 2
• Second Number = 3x = 3×2 = 6
• Third Number = 5x = 5 × 2 = 10

Answer 2

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