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A wholesaler purchased electric goods for the taxable amount of Rs. 1,50,000. He sold it to the retailer for the taxable amount of Rs. 1,80,000. Retailer sold it to the customer for the taxable amount of Rs. 2,20,000. Rate of GST is 18%. Show the computation of GST in tax invoices of sales. Also find the payable CGST and payable SGST for wholesaler and retailer.
If $\alpha$ and $\beta$ are the roots of $x^2+5 x-1=0$ then find :
1. $\alpha^3+\beta^3$
2. $\alpha^2+\beta^2$.
→1. $\alpha^3+\beta^3$
2. $\alpha^2+\beta^2$.
A line is parallel to one side of triangle which intersects remaining two sides in two distinct points then that line divides sides in same proportion.
Given: In $\triangle A B C$ line I || side $B C$ and line I intersect side $A B$ in $P$ and side $A C$ in $Q$.
To prove: $\frac{ AP }{ PB }=\frac{ AQ }{ QC }$
Construction: Draw $CP$ and $BQ$
Proof: $\triangle APQ$ and $\triangle PQB$ have equal height.
$\left.\frac{ A (\Delta APQ )}{ A (\Delta PQB )}=\frac{[}{ PB } \quad \ldots . . \text { (i) [areas in proportion of base }\right]$
$\frac{ A (\Delta APQ )}{ A (\Delta PQC )}=\frac{[}{ QC } \ldots . . . \text { (ii) [areas in proportion of base] }$
$\triangle P Q C$ and $\triangle P Q B$ have [____ ] is common base.
Seg PQ \| Seg BC, hence height of $\triangle A P Q$ and $\triangle P Q B$.
$A (\triangle PQC )= A (\Delta \ldots, \ldots \text {.....(iii) }$
$\frac{ A (\Delta APQ )}{ A (\Delta PQB )}=\frac{ A (\Delta \ldots)}{ A (\Delta \ldots \ldots[( i ) \text {, (ii), and (iii)] }}$
$\frac{ AP }{ PB }=\frac{ AQ }{ QC } \quad \ldots . . .[( i ) \text { and (iii)] }$
→Given: In $\triangle A B C$ line I || side $B C$ and line I intersect side $A B$ in $P$ and side $A C$ in $Q$.
To prove: $\frac{ AP }{ PB }=\frac{ AQ }{ QC }$
Construction: Draw $CP$ and $BQ$
Proof: $\triangle APQ$ and $\triangle PQB$ have equal height.
$\left.\frac{ A (\Delta APQ )}{ A (\Delta PQB )}=\frac{[}{ PB } \quad \ldots . . \text { (i) [areas in proportion of base }\right]$
$\frac{ A (\Delta APQ )}{ A (\Delta PQC )}=\frac{[}{ QC } \ldots . . . \text { (ii) [areas in proportion of base] }$
$\triangle P Q C$ and $\triangle P Q B$ have [____ ] is common base.
Seg PQ \| Seg BC, hence height of $\triangle A P Q$ and $\triangle P Q B$.
$A (\triangle PQC )= A (\Delta \ldots, \ldots \text {.....(iii) }$
$\frac{ A (\Delta APQ )}{ A (\Delta PQB )}=\frac{ A (\Delta \ldots)}{ A (\Delta \ldots \ldots[( i ) \text {, (ii), and (iii)] }}$
$\frac{ AP }{ PB }=\frac{ AQ }{ QC } \quad \ldots . . .[( i ) \text { and (iii)] }$
The loans sanctioned by a bank for construction of farm ponds are shown in the following table. Find the mean of the loans.
The following frequency distribution table shows the amount of aid given to 50 flood affected families. Find the mean of the amount of aid.
| Amount of aid (Thosand rupees) | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of families | 7-Jan | 13-Jan | 20-Jan | 6-Jan | 4-Jan |
The distances covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distances.
A frequency distribution of funds collected by 120 workers in a company for the drought affected people are given in the following table. Find the mean of the funds by 'step deviation' method.
| Fund (Rupees) | 0-500 | 500-1000 | 1000-1500 | 1500-2000 | 2000-2500 |
| No. of workers | 35 | 28 | 32 | 15 | 10 |
In the adjoining figure, XY || seg AC. If 2 AX = 3 BX and XY = 9, complete the activity to find the value of AC.
The prices of different articles and demand for them is shown in the following frequency distribution table. Find the median of the prices.
| Price (Rupees) | 20 less than | 20-40 | 40-60 | 60-80 | 80-100 |
| No. of articles | 140 | 100 | 80 | 60 | 20 |
Complete the following table.
→| Equation | No. of variables | whether linear or not |
| $\frac{3}{x}-\frac{4}{y}=8$ | 2 | Not linear |
| $\frac{6}{x-1}+\frac{3}{y-2}=0$ | ⬜ | ⬜ |
| $\frac{7}{2 x+1}+\frac{13}{y+2}=0$ | ⬜ | ⬜ |
| $\frac{14}{x+y}+\frac{3}{x-y}=5$ | ⬜ | ⬜ |