Pair of Linear ...

Solve: $$\displaystyle \frac{20}{x\, +\, y}\, +\, \displaystyle \frac{3}{x\, -\,y}\, =\, 7$$ and $$\displaystyle \frac{8}{x\, -\, y}\, -\, \displaystyle \frac{15}{x\, +\, y}\, =\, 5$$

A and B both have some pencils. If A gives $$10$$  pencils to B, then B will have twice as many as A. And if B gives $$10$$  pencils to A, then they will have the same number of pencils. How many pencils does each has?

Divide 80 into two numbers, such that 5 times one number is equal to 3 times the other number.

$$A$$'s age is twice as $$B$$'s age. $$4$$ years ago, $$A$$ was three times as old as $$B$$. Find their present ages.

Divide $$32$$ into two parts such that if the larger is divided by the smaller, the quotient is $$2$$ and the remainder is $$5$$.

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 ?

Divide 184 into two parts such that one- third of one part may exceed one-seventh of the other part by 4.

Two articles $$A$$ and $$B$$ are sold for Rs. $$1,167$$ making $$5\%$$ profit on $$A$$ and $$7\%$$ profit on B. If the two articles are sold for Rs. $$1,165$$, a profit of $$7\%$$ is made on $$A$$ and a profit of $$5\%$$ is made on $$B$$. Find the cost price of each article.

The class XI students of a school wanted to give a farewell party to the out going students of class XII. They decided to purchase two kinds of sweets, one costing Rs. 250 per kg and the other costing Rs. 350 per kg. They estimated that 40 kg of sweets were needed. if the total budget for the sweets was Rs. 11,800; find how much sweets of each kind were bought ?