Jitender Gupta and Divya Malik Solutions for Exercise 5: ARCHIVES (Last 8 Years)

$₹7500$ were divided equally among a certain number of children. Had there been $20$ less children, each would have received $₹100$ more. Find the original
number of children.

A bus covers a distance of $240 \mathrm{km}$ at a uniform speed. Due to heavy rain, its speed gets reduced by $10 \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.$ and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be $x \raisebox{1ex}{$\mathrm{km}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{h}$}\right.$, form an equation and solve it to evaluate $x$.

The sum of two natural numbers is $8$ and the difference of their reciprocals is $\frac{2}{15}$. Find the numbers.

Solve${\left(x-1\right)}^2-3x+4=0$ for $x$ using the quadratic formula. Write your answer correct to two significant figures.

A two-digit positive number is such that the product of its digits is $6$. If $9$ is added to the number, then the digits interchange their places. Find the number

Solve the following and calculate the answer correct to two decimal places.

$x^2-5x-10=0$

A car covers a distance of $400 km$ at a certain speed. Had the speed been$12 km/h$ more, the time taken for the journey would have been$1 h 40 min$ less. Find the original speed of the car in $km/hr$.

$₹480$ is divided equally among $x$ children. If the number of children was $20$ more than each would have got $₹12$ less. Find the value of $x$.