Question

The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was found to be ₹ 600. If cost of 1 kg of apples and 1 kg of grapes is ₹ x and ₹ y respectively, represent the given situation algebraically as a system of equations and check whether the system so obtained is consistent or not.

Solve for x and y : √2 x + √3 y = 5 and √3 x − √8 y = −√6

A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹ 50 and for each table is ₹ 200. The school spends ₹ 30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300. If the school rents 'x' chairs and 'y' tables, answer the following questions :

A fraction becomes 5/7 if 2 is added to both numerator and denominator. If 1 is subtracted from both, it becomes 1/2. Find the fraction.