Question

The average of the three numbers 83, 8Φ and Φ6 is 82. If the digit in the place of Φ is
the same, then find the digit in place.


Please give explanation ​

Answer 1

So we're given three numbers 83, 8x and x6 whose average is 82.

We've to find the value of x.

We know a two-digit number 'ab' can be written as 10a + b.

Thus 8x can be written as 10 × 8 + x = 80 + x.

Similarly, x6 can be written as 10x + 6.

Average of the three numbers, i.e., 82, is given by,

$\longrightarrow\dfrac{83+8x+x6}{3}=82$

$\longrightarrow\dfrac{83+(80+x)+(10x+6)}{3}=82$

$\longrightarrow83+80+x+10x+6=82\times3$

$\longrightarrow11x+169=246$

$\longrightarrow x=\dfrac{246-169}{11}$

$\longrightarrow\underline{\underline{x=7}}$

Hence 7 is the answer.

Answer 2

Answer:

Average of three numbers is 82, In other words all Number have to be 82 when distributed equally.

• 1st Number = 83 ; we will get 1 from here as 82 is Average.

Now 2nd Number is already started from 8Φ so It will already be near by 82.

So Let's add that 1 into 3rd Number to make it Φ7 i.e. from (Φ6 + 1)

Now we Need (82 - Φ7) = Φ5 to make it Average.

We will Take that from 2nd Number, But it will bring it's average number too ; so 3rd Number should give (5 + 2) = 7 to make it Average.

That will Give 8Φ = 87 and Φ6 = 76

∴ Hence, Digit at that place would be 7.