Embibe Experts Solutions for Chapter: Linear Equation, Exercise 1: Solving simultaneous equations

$Rs.417$ is divided among $A$, $B$, $C,$ and $D$ in such a way that $A$ gets $Rs.13$ more than $B$, $B$ gets $Rs.9$ more than $C$ and $C$ gets $Rs.6$ more than $D$. Find $A$'s share.

Preksha has $x$ notes of $50$ rupee denomination and $3x$ notes of $20$ rupee denomination. The total amount with her is equal to $\left(x+4\right)$ notes of $50$ rupee denomination and $\left(x+14\right)$ notes of $20$ rupee denomination. Find the value of $3x$.

The total cost of $11$ chairs and $8$ tables is $Rs. 9,450$. If the cost of one chair is equal to $\frac{1}{3}$rd of the cost of each table, what is the total cost of $6$ chairs?

If  $2x+5y=109$ and $2x+5=y+12$ then $y-x=?$

A zoo has few number of penguins and polar bears. The total number of heads of both of them is $60$ and total number of their feet is $160$. How many polar bears are there in the zoo?

How many solutions will a pair of linear equations have, if the equations are $4x+5y-6=0$ and $16x+20y+20=0$?

If $\frac{ 6x-1}{x}+\frac{ 7y-1 }{y}+\frac{8z-1}{z}=0$, then what is the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$?

The population of Patna city is $96000$, the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$, the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?