Q.7 Journalise the following transactions; post them into Ledger for February 2019
1 Sunil Started business with stock of goods ` 20,000 and Cash ` 1,70,000 out of which ` 50,000
borrowed from his friend Kedar@10 p.a.
5 Placed an order for goods worth ` 7,000 with Mohan for which advance ` 5,500 was paid.
9 Purchased Stationery for office use ` 4,500
12 Goods distributed as free samples ` 2,000
17 Paid Freight ` 400 on behalf of Mr. Dev.
24 Received Goods from Mohan as per our order dated 5th Feb and settled his account.
27 Bought goods from Shekhar on two months credit for ` 7,000 at 20% Trade Discount with
instructions to send them to Sagar.
28 Sent to Sagar Outward Invoice for goods supplied by Shekhar. at list price less 10% Trade
Discount.
Answers
Answer:
\large\underline{\sf{Solution-}}
Solution−
Let assume that
\begin{gathered}\rm \: \alpha ,\gamma \: be \: the \: roots \: of {3x}^{2} - 2x - 5 = 0 \\ \end{gathered}
α,γbetherootsof3x
2
−2x−5=0
Consider,
\begin{gathered}\rm \: {3x}^{2} - 2x - 5 = 0 \\ \end{gathered}
3x
2
−2x−5=0
\begin{gathered}\rm \: {3x}^{2} - 5x + 3x - 5 = 0 \\ \end{gathered}
3x
2
−5x+3x−5=0
\begin{gathered}\rm \: x(3x - 5) + 1(3x - 5) = 0 \\ \end{gathered}
x(3x−5)+1(3x−5)=0
\begin{gathered}\rm \: (x + 1)(3x - 5) = 0 \\ \end{gathered}
(x+1)(3x−5)=0
\begin{gathered}\rm\implies \:x = - 1 \: \: or \: \: x = \dfrac{5}{3} \\ \end{gathered}
⟹x=−1orx=
3
5
\begin{gathered}\rm\implies \: \gamma = - 1 \: \: or \: \: \alpha = \dfrac{5}{3} \\ \rm \: or \\ \rm\implies \: \alpha = - 1 \: \: or \: \: \gamma = \dfrac{5}{3} \\\end{gathered}
⟹γ=−1orα=
3
5
or
⟹α=−1orγ=
3
5
Now,
Let assume that,
\begin{gathered}\rm \: \alpha, \beta \: be \: the \: roots \: of \: {2x}^{2} + px - 1 = 0 \\ \end{gathered}
α,βbetherootsof2x
2
+px−1=0
We know,
\begin{gathered}\boxed{\red{\sf Sum\ of\ the\ roots=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}} \\ \end{gathered}
Sum of the roots=
coefficient of x
2
−coefficient of x
\begin{gathered}\rm\implies \: \alpha + \beta = - \dfrac{p}{2} \\ \end{gathered}
⟹α+β=−
2
p
Also,
\begin{gathered}\boxed{\red{\sf Product\ of\ the\ roots=\frac{Constant}{coefficient\ of\ x^{2}}}} \\ \end{gathered}
Product of the roots=
coefficient of x
2
Constant
\begin{gathered}\rm\implies \: \alpha \beta = - \dfrac{1}{2} \\ \end{gathered}
⟹αβ=−
2
1
It means, we have
\begin{gathered}\rm\implies \: \alpha + \beta = - \dfrac{p}{2} \: \: and \: \: \alpha \beta = - \dfrac{1}{2} \\ \end{gathered}
⟹α+β=−
2
p
andαβ=−
2
1
Case :- 1
\begin{gathered}\rm \: \alpha = - 1 \\\end{gathered}
α=−1
As, we have
\begin{gathered}\rm \: \alpha \beta = - \dfrac{1}{2} \\ \end{gathered}
αβ=−
2
1
\begin{gathered}\rm \: ( - 1) \beta = - \dfrac{1}{2} \\ \end{gathered}
(−1)β=−
2
1
\begin{gathered}\rm \:\beta = \dfrac{1}{2} \\ \end{gathered}
β=
2
1
Now,
\begin{gathered}\rm \: \alpha + \beta = - \dfrac{p}{2} \\ \end{gathered}
α+β=−
2
p
\begin{gathered}\rm \: - 1 + \dfrac{1}{2} = - \dfrac{p}{2} \\ \end{gathered}
−1+
2
1
=−
2
p
\begin{gathered}\rm \: - \dfrac{1}{2} = - \dfrac{p}{2} \\ \end{gathered}
−
2
1
=−
2
p
\begin{gathered}\rm\implies \:p \: = \: 1 \\ \end{gathered}
⟹p=1
Now, Consider Case :- 2
\begin{gathered}\rm \: \alpha = \dfrac{5}{3} \\\end{gathered}
α=
3
5
As, we have
\begin{gathered}\rm \: \alpha \beta = - \dfrac{1}{2} \\ \end{gathered}
αβ=−
2
1
\begin{gathered}\rm \: \frac{5}{3} \times \beta = - \dfrac{1}{2} \\ \end{gathered}
3
5
×β=−
2
1
\begin{gathered}\rm \: \beta = - \dfrac{3}{10} \\ \end{gathered}
β=−
10
3
Now,
\begin{gathered}\rm \: \alpha + \beta = - \dfrac{p}{2} \\ \end{gathered}
α+β=−
2
p
\begin{gathered}\rm \: \dfrac{5}{3} - \dfrac{3}{10} = - \dfrac{p}{2} \\ \end{gathered}
3
5
−
10
3
=−
2
p
\begin{gathered}\rm \: \dfrac{50 - 9}{30} = - \dfrac{p}{2} \\ \end{gathered}
30
50−9
=−
2
p
\begin{gathered}\rm \: \dfrac{41}{30} = - \dfrac{p}{2} \\ \end{gathered}
30
41
=−
2
p
\begin{gathered}\rm\implies \:p \: = \: - \: \dfrac{41}{15}\\ \end{gathered}
⟹p=−
15
41
So,
\begin{gathered}\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\bf{p \: = \: 1} \\ \\ &\sf{or}\\ \\ &\bf{p \: = \: - \: \dfrac{41}{15} } \end{cases}\end{gathered}\end{gathered}\end{gathered}
⟹
⎩
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎧
p=1
or
p=−
15
41
\rule{190pt}{2pt}
Additional Information :-
Nature of roots :-
Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.
If Discriminant, D > 0, then roots of the equation are real and unequal.
If Discriminant, D = 0, then roots of the equation are real and equal.
If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.
Where,
Discriminant, D = b² - 4ac
Explanation:
assdf