Abhijit Guha Solutions for Chapter: Linear Equations, Exercise 1: Practice Problems Level 1

A man was allotted a work for $30$ days on the condition that he would get $₹10$ per day as wage if he reports for work and if he remains absent he would have to pay $₹2$ as penalty for one day. Ultimately, he got $₹216$. Find how many days he remained absent:

Divide $243$ into three parts such that half of the first part, one-third of the second part and one-fourth of the third part, shall be equal:

A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was $₹1,500$ after four years of service and $₹1,800$ after ten years of service, then the annual increment was_____.

A car is filled with $7 \mathrm{L}$ of oil for full round trip fuel is taken $\frac{1}{3} \mathrm{L}$ more in going than coming. What is the fuel consumed in coming up?

If $2$ oranges, $3$ bananas and $5$ apples cost $₹30$ and $4$ oranges, $3$ bananas and $1$ apple cost $₹18$, then the cost of $3$ oranges, $3$ bananas and $3$ apples will be_____.

A, B, C, D have $₹2900$ between them. A has twice as much as C and B has three times as much as D. C and D together have $₹500$ less than A. The difference of A's share and D's share will be_____.

In a box containing red and white marbles, half the number of white ones is equal to a third of the number of red, and twice the whole number of marbles exceeds three times the number of red marbles by four. The total number of marbles (n) in the box should be______.

In what year would an employee joined in $1985$ on his $30\mathrm{th}$ age be eligible to retire from the company, which has a retirement rule such as an employee to retire when the difference between employee's age when he hired by the company and years of employment with the company is $6$: