R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 13: EXERCISE 4.13

If the list price of a toy is reduced by $₹2$, a person can buy $2$ toys more for $₹360$. Find the original price of the toy. (Use the symbol $₹$)

$₹9000$ were divided equally among a certain number of persons. Had there been $20$ more persons, each would have got $₹160$ less. Find the original number of persons.

Some students planned a picnic. The budget for food was $₹500$. But $5$ of them failed to go and thus the cost of food for each member increased by $₹5$. How many students attended the picnic $?$

A pole has to be erected at a point on the boundary of a circular park of diameter $13$ metres in such a way that the difference of its distances from two diametrically opposite fixed gates $\mathrm{A}$ and $\mathrm{B}$ on the boundary is$7$ metres. If the distance of the pole from the gate $\mathrm{B}$ be $x$ metres, then find the value of $x$.

In a class test, the sum of the marks obtained by $\mathrm{P}$ in Mathematics and Science is $28$. Had he got $3$ marks more in Mathematics and $4$ marks less in Science. The product of his marks, would have been$180$. Find his marks in the two subjects.

In a class test, the sum of Shefali's marks in Mathematics and English is $30$. Had she get $2$ marks more in Mathematics and $3$ marks less in English, the product of their marks would have been$210$. Find her marks in the two subjects.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was $3$ more than twice the number of articles produced on that day. If the total cost of production on that day was $₹90$, find the number of articles produced and the cost of each article.

At $t$ minutes past $2 \mathrm{pm}$, the time needed by the minutes hand and a clock to show $3 \mathrm{pm}$ was found to be $3 \mathrm{minutes}$ less than $\frac{t^2}{4} \mathrm{minutes}$. Find $t$.