Question

(a) Solve the following inequation and write the solution set :

$13x-5<15x+4<7x+12,x\in R$

Represent the solution on a real number line.
$\left[3\right]$

(b) The MP of an article = ₹900 and rate of GST on it is 18%. A shopkeeper buys this article at a reduced price and sells it at its marked price. If the shopkeeper pays ₹16.2 as CGST to the government as part of his net tax liability, find the amount (exclusive of GST) paid by the shopkeeper.
$\left[3\right]$

(c) Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs 1,200 as interest at the time of maturity, find :

(i) the monthly instalment

(ii) the amount of maturity.
$\left[4\right]$

Answer 1

(a)

$\left[3\right]$

(b) Let the shopkeeper buy the article at ₹x

For him CP = ₹x and SP = ₹900
$\left[0.5\right]$

Net CGST paid to the government = ₹16.2, hence Net SGST paid to the government = ₹16.2
$\left[0.5\right]$

So, total GST paid = ₹16.2 + ₹16.2 = ₹32.4
$\left[0.5\right]$

GST on Output - GST on Input = ₹32.4
$\left[0.5\right]$

$\Rightarrow$18% of ₹900 - 18% of ₹x = ₹32.4
$\left[0.5\right]$


$\Rightarrow$ $\frac{18x}{100}$ = ₹ 162 - ₹32.4 = ₹129.6

$\Rightarrow$ x = ₹720

Hence, the amount paid by the shopkeeper is ₹720.
$\left[0.5\right]$

(c) (i) P = Rs. 1200,

n = 2 x 12 = 24 months,
r = 6%
$\left[0.5\right]$

Interest = $P\times \frac{n(n+1)}{2\times 12}\times \frac{r}{100}$
$\left[0.5\right]$

⇒$1200=P\times \frac{24(24+1)}{2\times 12}\times \frac{6}{100}$

⇒$1200=P\times \frac{3}{2}$

⇒$P=1200\times \frac{2}{3}$

⇒ $P=Rs800$

So the monthly instalment is Rs. 800.
$\left[1\right]$

(ii) Total sum deposited = $P\times n=Rs.800\times 24=Rs.19200$
$\left[1\right]$

∴ Amount of maturity = Total sum deposited + Interest on it

= Rs. 19200 + Rs. 1200

= Rs 20400
$\left[1\right]$