Pair of Linear ...

A man has only $$20$$ paise coins and $$25$$ paise coins in his purse. If he has $$50$$ coins in all totaling Rs. $$11.25$$, how many coins of each kind does he have?

The sum of two numbers is $$8$$. If their sum is $$4$$ times their difference. Find the numbers.

The sum of the numerator and denominator of a fraction is $$4$$ more than twice the numerator. If the numerator and denominator are increased by $$3$$, they are in the ratio $$2 : 3$$. Determine the fraction

Draw the graphs of the equations $$x = 3, x = 5$$ and $$2x - y - 4 = 0$$. Also find the area of the quadrilateral formed by the lines and the x-axis

A and B each have a certain number of mangoes. A says to B," if you give 30 of your mangoes, I will have twice as many as left with you."B replies,"if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?

$$4$$ tables and $$3$$ chairs together cost Rs. $$2250$$ and $$3$$ tables and $$4$$ chairs cost Rs. $$1950$$. Find the cost of $$2$$ chairs and $$1$$ table.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. $$27$$ for a book kept for seven days, while Susy paid Rs. $$21$$ for the book she kept for five days. Find the fixed charge and the charge for each extra day.

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?