Application of Equations

A student gets $4$ marks for each correct sum and loses $1.5$ marks for each incorrect sum. He does $24$ sums and obtains $46.5$ marks. What was the number of correct and incorrect sums?

 The sum of two consecutive multiples of $4$ is $60$. Find the number.

The length of a rectangle is twice its breadth. If the perimeter is $90$ metres, find the length and breadth of the rectangle.

Divide $56$ into two parts, so that thrice of the first part becomes $48$ more than one third of the second part.

My uncle changed a $1000$ rupee cheque from a bank in the form $5$ rupee and $10$ rupee notes. If he received $137$ notes in total then find the number of $5$ rupee notes that he got.

Find three consecutive odd numbers whose sum is $81$.

Find the numbers such that three fifth of one number diminished by one tenth of the other number which is $5$ less than the first number, gives $25$.

$A$ and $B$ are friends and their ages differ by $2$ years. $A\text{'}s$ father $D$ is twice as old as $A$ and $B$ is twice as old as his sister $C$. The age of $D$ and C differ by $40$ years. Find the ages of $40$ and $B$.

A daughter is one-fourth her father’s age at present. If after $5$ years, the daughter becomes one-third of her father’s age. Then, calculate their present ages.

Michael and Tom are brothers. Their combined age is $20$, and Tom is $4$ years older than Michael. What are Michael and Tom's ages?

The sum of two numbers is $15$. The difference of the same two numbers is $7$. What are the two numbers?

One number is half of the other. Sum of these two numbers is equal to $6$. Then the two numbers are

Ten years ago father was $12$ times as old as his son and $10$ years hence he will be twice as old as his son. Find their present ages. 

$5$ pens and $6$ pencils together cost $₹9$ and $3$ pens and $2$ pencils cost $₹5$. Find the cost of $1$ pen and $1$ pencil.

Five years ago, Neeta was trice as old as Reeta. Ten years later, Neeta will be twice as old as Reeta, How old are Neeta and Reeta now?

Ram’s age is three times the sum of the ages of his two sons. After $5$ years, his age will be twice the sum of the ages of his two sons. Find the age of Ram (in years).

The age of Ravi is three times the age of his son. After $3$ years, his age will be twice the age of his son. Find the age of Ravi (in years).

What is the present age of Ramesh (in years), if $10$ years ago he was $25$ years old?

Apoorv received three- fourths of all voted cast in the election for school president. If he received $876$ votes, then how many students voted?

The length of a rectangle is thrice its breadth. If the perimeter is $80$ metres, find the length of the rectangle.