Question

$\boxed{\bf1 } \rm\: solve \: and \: verify \: it \: : \\ \\ \: \: \tt2(x - 3) = \frac{3}{5} (x + 4)$
$\boxed{ \bf 2} \rm\: draw \: a \: rectangle \: and \: write \\ \rm \: all \: the \: properties \:.$
$\boxed{ \bf 3} \rm \: a \: shopkeeper \: sold \: an \\ \rm \: old \: pair \: of \: shoes \: at \: rs \: 480. \\ \rm \: if \: the \: marketed \: price \: is \: rs \: 600 \\ \rm \: find \: the \: rate \: of \: discount.$
​

Answer 1

Answer 1

Solution :

$\rm 2(x-3)=\dfrac{3}{5}(x+4) \\ \\ \rm5\times2(x-3)=3 (x+4) \\ \\ \rm10 (x-3) = 3(x+4) \\ \\ \rm10x-30 = 3x + 12 \\ \\ \rm10x-3x= 12+30 \\ \\ \rm7x= 42 \\ \\ \rm x= \dfrac{42}{7} \\ \\ \bf x=6 \\ \\ \therefore \sf Required \: solution \: is \: x= \bf6$

Verification :

$\rm LHS \: = 2(x - 3) \\ = 2(6 - 3) \\ = 2 \times 3 \\ \bf = 6 \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \rm RHS = \frac{3}{5} (x + 4) \\ = \frac{3}{5} (6 + 4) \\ = \frac{3}{5} \times10 \\ = 3 \times 2 \\ = \bf6$

Since, LHS = RHS

Therefore, 6 is the solution of the equation.

Answer 2

Drawing :

$\huge \boxed{ \begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}}$

Properties of rectangle :

• Opposite sides are equal and parallel.
• Opposite angles are equal.
• Adjacent angles are supplementary.
• The diagonals bisect each other at the point of their interesection.
• Each of the angles is a right angle.
• Diagonals are equal.

Answer 3

Solution :

For the pair of shoes, MP = Rs 600

SP= Rs 480

Therefore, Discount = MP - SP = Rs (600 - 480) = Rs 120

When MP is Rs 600, amount of discount = Rs 120

$\small\boxed{\therefore \bf When\: MP\: is \:Rs\: 1, amount \: of\: discount = Rs \dfrac{120}{600}} \\ \\ \rm \small\therefore When \:MP\: is \:100, amount \:of\: discount = Rs \dfrac{120}{600} \times 100 \\ \large \bf= Rs \: 20$

Therefore, the rate of discount = 20%