for 2100 member team consisting of team leaders and athletes is attending the National athletic mate. For every 20 athletes there is one team leader, how many team leaders would be there The team?
Answers
Step-by-step explanation:
Answer:
\bf \underline{The\ original\ number\ is\ 92.}
The original number is 92.
Step-by-step explanation:
Let the digit at tens and units place be x and y respectively.
Amd the number be (10x+y)
Given
Product of digit is 18.
So,
ATE, xy=18
or y=18/x -(1)
Also, when 63 is subtracted from the number, the digits interchange their place.
So, the number formed by interchanging the digits is (10y+x)
ATE,
(10x+y)-63=(10y+x)
10x-x+y-10y=63
9x-9y=63
9(x-y)=63
x-y=7 -(2)
Using y=18/x in eq. (2)
\begin{lgathered}x-\frac{18}{x}=7\\ \\ \implies \rm x^2-18=7\\ \\ \implies \rm \frac{x^2-18}{x}=7\\ \\ \implies \rm x^2-7x-18=0\\ \\ \implies \rm x^2-9x+2x-18=0\\ \\ \implies \rm x(x-9) 2(x-9)=0\\ \\ \implies \rm (x+2) (x-9)=0\\ \\ \implies \bf x=-2\ or\ \bf 9 \\ \rm But\ digit\ can't\ be\ negative.\\ \therefore \bf x=9\end{lgathered}
x−
x
18
=7
⟹x
2
−18=7
⟹
x
x
2
−18
=7
⟹x
2
−7x−18=0
⟹x
2
−9x+2x−18=0
⟹x(x−9)2(x−9)=0
⟹(x+2)(x−9)=0
⟹x=−2 or 9
But digit can
′
t be negative.
∴x=9
Putting x=9 in eq. (1)
9y=18
y=2
So, the number is (10×9+2)=90+2=92