R K Bansal Solutions for Exercise 1: EXERCISE

$90\%$ acid solution ( $90\%$ pure acid and $10\%$ water) and $97\%$ acid solution are mixed to obtain $21$ litres of $95\%$ acid solution. How many litres of each solution are mixed.

Class $XI$ students of a school wanted to give a farewell party to the outgoing students of class $XII$. They decided to purchase two kinds of sweets, one costing $₹250$ per $\mathrm{kg}$ and the other costing $₹350$ per $\mathrm{kg}$. They estimated that $40 \mathrm{kg}$ of sweets were needed. If the total budget for the sweets was $₹11,800$, find how much sweets of each kind were bought?

Mr. and Mrs. Ahuja weigh $x \mathrm{kg}$ and $y \mathrm{kg}$ respectively. They both take a dieting course, at the end of which Mr. Ahuja loses $5 \mathrm{kg}$ and weighs as much as his wife weighed before the course. Mrs. Ahuja loses $4 \mathrm{kg}$ and weighs $\frac{7}{8}$ of what her husband weighed before the course. Form two equations in $x$ and $y$ to find their weights before taking the diet course.

A part of monthly expenses of a family is constant and the remaining vary with the number of members in the family. For a family of $4$ persons, the total monthly expenses are $₹10,400$, whereas for a family of $7$ persons, the total monthly expenses are $₹15,800$. Find the constant expenses per month and the monthly expenses on each member of a family.

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10 \mathrm{km}$, the charge paid is $₹315$ and for a journey of $15 \mathrm{km}$, the charge paid is $₹465$. What are the fixed charges and the charge per $\mathrm{kilometer}$? How much does a person have to pay for travelling a distance of $32 \mathrm{km}$?

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Geeta paid $₹27$ for a book kept for seven days, while Mohit paid $₹21$ for the book he kept for five days. Find the fixed charges and the charge for each extra day.

The area of a rectangle gets reduced by $9$ square units, if its length is reduced by $5$ units and breadth is increased by $3$ units. However, if the length of this rectangle increases by $3$ units and the breadth by $2$ units, the area increases by $67$ square units. Find the dimensions of the rectangle.

It takes $12$ hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for $4$ hours and the pipe of smaller diameter is used for $9$ hours, only half of the pool is filled. How long would each pipe take to fill the swimming pool?