R. D. Sharma Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 11: EXERCISE 3.11

There are two examination rooms $A$ and $B.$ If $10$ candidates are sent from $A$ to $B,$ the number of students in each room is same. If $20$ candidates are sent from $B$ to $A,$ the number of students in $A$ is double the number of students in $B.$ Find the number of students in each room.

A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs $₹216$ and one full and one half reserved first class tickets cost $₹327.$ What is the basic first class full fare and what is the reservation charge?

A wizard having powers of mystic in conditions and magical medicines seeing a cock, fight going on, spoke privately to both the owners of cocks. To one, he said; ''If your bird wins, then you give me your stake-money, but if you do not win, I shall give you two third of that.'' Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only $12$ gold coins. Find the stake of money each of the cock-owners have.

The students of a class are made to stand in rows. If $3$ students are extra in a row, there would be $1$ row less. If $3$ students are less in a row there would be $2$ rows more. Find the number of students in the class.

One says, "Give me 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?

A shopkeeper sells a saree at $8\%$ profit and a sweater at $10\%$ discount, thereby getting a sum of $₹1008$. If she had sold the saree at $10\%$ profit and the sweater at $8\%$ discount, she would have got $₹1028$. Find the cost price of the saree and the list price (price before discount) of the sweater.

In a competitive examination, one mark is awarded for each correct answer while $1/2$ mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$ marks. How many questions did she answer correctly.

A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid $₹22$ for a book kept for $6$ days, while Anand paid $₹16$ for the book kept for four days. Find the fixed charges and charge for each extra day.