Question

In the five digit number 13 ab4, a is the greatest single digit perfect cube and a is four times of b, then the sum of the number and its cube root is 138xy. Find xy (two digit number).​

Answer 1

Answer:

48

Step-by-step explanation:

Single digit perfect cubes are 1³(=1) and 2³(=8)  &  greatest of these cubes is 8(=2³).

 ∴ a = greatest single digit perfect cube

    a = 8

Given, 'a' is 4 times of b.    Therefore,

 ⇒ a = 4b       ⇒ 8 = 4b        ⇒ 2 = b

∴ Number is 13ab4 = 13824.   Cube root of 13824 is 24.

  Hence,

sum of number and its cube root is

    = 13824 + 24

    = 13848

Comparing this with question,  

⇒  13848 = 138xy

⇒ 48 = xy

Hence the required value of 'xy' is 48

Answer 2

Given :- In the five digit number 13 ab4, a is the greatest single digit perfect cube and a is four times of b. The sum of the number and its cube root is 138xy.

To Find :- xy (two digit number).

Solution :-

Single digit perfect cubes are :-

• 1³ = 1
• 2³ = 8
• 8 > 1 .

So,

→ Greatest single digit perfect cube = a = 8

then,

→ b = 8/4 = 2 { since a is four times of b. }

then,

→ Given five digit number = 13ab4 = 13824

now,

→ Given number + (Given number)^(1/3) = 138xy

→ 13824 + (13824)^(1/3) = 138xy

→ 13824 + (24³)^(1/3) = 138xy

→ 13824 + (24)^(3 * 1/3) = 138xy

→ 13824 + 24 = 138xy

→ 13848 = 138xy

therefore,

→ xy (two digit number) = 48 (Ans.)

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