Question

What number multiplied by 3, then increased by 3/4 of the product, then divided by 7, then diminished by 1/3 of the result, then multiplied by itself, then diminished by 52, whose square root is then extracted before 8 is added, and then divided by 10, gives the final result of 2?

Answer 1

Let the number be x
Now, going according to word of maiden ,
The number is multiplied by 3 and decreased by 3/4
So, x * 3 + 3/4 ( 3x )
= 21/4x

Then, divided by 7 and diminished by 1/3 of quotient,
21x/4 ÷ 7 = 3x/4
3x/4 - 1/3 ( 3x/4)
= 2/3 ( 3/4 ) x
= x/2

Multiplied by itself,
= x/2 * x/2
= x²/4
Now diminished by 52
= √ ( x²/4 - 52 )
Then added 8 , divided by 10
= [ √ ( x²/4 - 52 ) + 8 ] / 10

According to the question,
[ √ ( x²/4 - 52 ) + 8 ] / 10 = 2
√( x²/4 - 52 ) + 8 = 20
√(x²/4 -52 ) = 12
x²/4 - 52 = 144
x²/4 = 144 + 52
x²/4 = 196
(x/2)² = 14²
x/2 = 14
x = 2 * 14
x = 28 .