Question

Vikas has $Rs(x^3+2ax+b)$, with this money he can buy exactly $(x-1)$ jeans or $(x+1)$ shirts with no money left. How much money Vikas has, if $x=4$?

• A. $Rs80$
• B. $Rs120$
• C. $Rs30$
• D. $Rs60$

Answer 1

The correct option is D $Rs60$

Vikas has Rs $(x³+2ax+b)$ .

Case 1 :- He can buy exactly $(x-1)$ jeans

means, Rs $(x³+2ax+b)$ is divisible by $(x-1)$

or you can say that $x=1$ is zero of $(x³+2ax+b)$

Now, put $x=1$ in $x³+2ax+b$

e.g., $1³+2a.1+b=0$

$2a+b=-1$ --------(1)

Case 2 :- he can also buy exactly $(x+1)$ shirts

means, Rs $(x³+2ax+b)$ is divisible by $(x+1)$

or, you can say that $x=-1$ is zero of $(x³+2ax+b)$

now , put $x=-1$ in $x³+2ax+b$

e.g., $-1-2a+b=0$

$-2a+b=1$ ------(2)

Solveequations(1)and(2),

$2b=0\Rightarrow b=0$ and $a=\frac{-1}{2}$

So, vikas has Rs.$(x^3-x)$. Now,at $x=4,$ vikas has Rs$(4^3-4)=60$