Question

Two whole numbers are such that the cube of first number exceeds the cube of second by 61 and the ratio of the numbers is 5:4. What is the value of larger number?

A) 3 B) 4 C) 5 D) 6​

Answer 1

Answer:

Option D

6

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Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Cube of first number exceeds the cube of second number by 61.

•Ratio of the numbers is = 5 : 4

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's value of larger number?

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let the two numbers be 5x and 4x.

Given that,

The cube of first number exceeds the cube of second by 61.

Therefore,

⟶ (5x)³ - (4x)³ = 61

⟶ 125x³ - 64x³ = 61

⟶ 61x³ = 61

⟶ x³ = 1

⟶ x = 1

Hence,

Larger number

= 5x ( Putting the value of x)

= 5 × 1

= 5

____________________________________________

Verification :-

Given that,

The cube of first number exceeds the cube of second by 61.

⟶ (5x)³ - (4x)³ = 61

⟶ (5 × 1)³ - (4 × 1)³ = 61

⟶ 61 = 61

L.H.S = R.H.S

(Verified)