Question 1 :
From a bus stand in Bangalore , if we buy 2 tickets to Malleswaram and 3 tickets to Yeshwanthpur, the total cost is Rs. 46; but if we buy 3 tickets to Malleswaram and 5 tickets to Yeshwanthpur the total cost is Rs. 74. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur.

Question 2 :
One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?

Question 3 :
Solve the following pair of linear equations by the substitution method : $s - t = 3 ; \frac{s}{3} + \frac{t}{2} = 6$

Question 4 :
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

Question 5 :
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Question 6 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are intersecting when _____________.

Question 7 :
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Question 9 :
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed are coincident lines.

Question 10 :
Solve the following pair of linear equations by the substitution method : $x + y = 14 ; x - y = 4$

Question 11 :
Champa went to a ‘Sale’ to purchase some pants and skirts. When her friends asked her how many of each she had bought, she answered, “The number of skirts is two less than twice the number of pants purchased. Also, the number of skirts is four less than four times the number of pants purchased”. Find how many pants and skirts Champa bought, graphically.

Question 12 :
In case of infinitely many solutions, the pair of linear equations is said to be __________.

Question 13 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then the pair of linear equations is _______.

Question 14 :
Is it true to say that the pair of equations – x + 2y + 2 = 0 and $\frac{1}{2}x-\frac{1}{4}y-1=0$ has a unique solution?

Question 15 :
Solve the following pair of linear equations by the substitution and cross-multiplication methods : $8x + 5y = 9 ; 3x + 2y = 4$

Question 17 :
The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pencil box.

Question 18 :
The difference between two numbers is 26 and one number is three times the other. Find them.

Question 19 :
Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received.

Question 20 :
In a ∆ ABC, ∠ C = 3 ∠ B = 2 (∠A + ∠ B). Find the three angles.