Question

(a) Solve equation, given below, using factorisation method:

$\frac{4}{x+2}-\frac{1}{x+3}=\frac{4}{2x+1}$
$\left[3\right]$

(b) P is the solution set of $7x-2>4x+1\text{and Q is the solution set of}9x-45\ge 5(x-5);wherex\in R$. Represent :

(i) $P\cap Q$

(ii) $P-Q$

(iii) $P\cap Q^{\prime }$ on different number lines.
$\left[3\right]$

(c) The following table shows the MRP of a few brands of motorcycles. If the GST charged on them is 18%, find the total price after GST of the motocycles.

$\begin{array}{cccccc}\text{Brand}& \text{Brand}& \text{Hero}& \text{Honda}& \text{Royal}& \text{TVS}\\ & \text{Pulsar}& \text{Xtreme}& \text{Unicorn}& \text{Enfield}& \text{Apache}\\ & & & & \text{Bullet}& \\ \text{MRP(in Rs)}& \text{95000}& \text{110000}& \text{90000}& \text{180000}& \text{120000}\\ \text{Discount \%}& \text{10}& \text{20}& \text{25}& \text{10}& \text{30}\end{array}$
$\left[4\right]$

Answer 1

(a)
$\left[3\right]$

(b)
$\left[1\right]$


$\left[1\right]$



$\left[1\right]$

(c)
$\begin{array}{cccc}\text{Brand}& \text{MRP (in Rs.)}& \text{Discount}\%& \text{Selling}\\ & & & \text{Price (After}\\ & & & \text{Discount)}\\ \text{Bajaj}& 95000& 10& 90\%of95000\\ \text{Pulsar}& & & =\frac{90}{100}\times 95000\\ & & & =85500\\ \text{Hero}& 110000& 20& 80\%of110000\\ \text{Xtreme}& & & =\frac{80}{100}\times 110000\\ & & & =88000\\ \text{Honda}& 90000& 25& 75\%of90000\\ \text{Unicorn}& & & =\frac{75}{100}\times 90000\\ & & & =67500\\ \text{Royal}& 180000& 10& 90\%of180000\\ \text{Enfield}& & & =\frac{90}{100}\times 180000\\ \text{Bullet}& & & =162000\\ \text{TVS}& 120000& 30& 70\%of120000\\ \text{Apache}& & & =\frac{70}{100}\times 120000\\ & & & =84000\end{array}$
$\left[2\right]$

Total Amount before GST = ₹85500 + ₹88000 + ₹67500 + ₹162000 + ₹84000 = ₹487000
$\left[0.5\right]$

GST = 18%

Total GST = $\frac{18}{100}\times 487000$ = ₹87660
$\left[0.5\right]$

$\therefore$Total Amount after GST = ₹487000 + ₹87660 = ₹574660
$\left[1\right]$