Pair of Linear Equations in Two Variables

90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution. Find the quantity of each type of acid to be mixed to form the mixture.

A railway half ticket costs half the full fare and the reservation charge is the some on half ticket as on full ticket. One reserved first class ticket from Mumbai to Delhi costs ₹4150 while one full and one half reserved first class ticket cost ₹ 6255. What is the basic first class full fare and what is the reservation charge?

A man sold a chair and a table together for Rs. 1520, thereby making a profit of 25% on chair and 10% on table. By selling them together for Rs. 1535, he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.

The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.

Find the value(s) of p in (i) to (iv) and p and q in (v) for the following pair of equations:

– x + py = 1 and px – y = 1,

if the pair of equations has no solution.

A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

Solve for x and y:
7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2

The present age of a woman is 3 years more than three times the age of her daughter. Three years hence, the woman’s age will be 10 years more than twice the age of her daughter. Find their present ages.