Applications of Pair of Linear Equations

If the product of two numbers is $320$ and their ratio is $1 : 5$, what is the difference between the squares of these two numbers?

The sum of six consecutive even numbers of Set $A$ is $402$. What is the sum of four consecutive numbers from another Set $B$ whose lowest number is $15$ less than double the lowest number of Set $A$?

Raman's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is $125$ years. What is the difference between the present ages of Raman's daughter and Raman's mother?

The sum of the present ages of father and son is $80 \mathrm{years}$. $4 \mathrm{years}$ ago, the ratio of their age was $2:1$. Father's present age will be-

Arpit can friends a garden in $3$ hours, Ankur can do it in $5$ hours and Akash take $6$ hours to do the same if they work together in how many hours can they fence the garden?

A test consists of 'True' or 'False' questions. One mark is awarded for every correct answer while $\frac{1}{4}$ mark is deducted for every wrong answer. A student knew the answers to some of the questions. Rest of the questions he attempted by guessing. He answered $120$ questions and got $90$ marks. 

If answers to all questions he attempted by guessing were wrong then how many questions did he answer correctly?

 Two years ago, my age was $4\frac{1}{2}$ times the age of my son. Six years ago, my age was twice the square of the age of my son. What is the present age of my son?

At a movie theatre, stall tickets are available at Rs. 100 and balcony tickets are available at Rs. 150. The total capacity of the theatre is 3000 seats, including both stall and balcony. The total revenue generated at the theatre when it was houseful is Rs. 4 lakh. Find the capacity of the stall.

Anuj had some chocolates, and he divided them into two lots $\mathrm{A}$ and $\mathrm{B}$. He sold the first lot at the rate of $₹2$ form $3$ chocolates and the second lot at the ratio $₹1$ per chocolate, and got a total of $₹400$. If he had sold the first lot at the rate of $₹1$ per chocolate, and the second lot at the rate of $₹4$ for $5$ chocolates, his total collection would have been $₹460$. Find the total number of chocolates he had.

The difference between two numbers is $10$. If one of the number is double the other number, find both the numbers.

A plane flying north at $500 mph$ passes over a city at $12$noon. A plane flying east at the sea altitude passes over the same city at $12:30$ P.M. The plane is flying east at $400 mph$. To the nearest hundred miles, how far apart the two planes at $2$ P.M.?

Swarna between 3:00 and 4:00, looked at her watch and noticed the time. After some time she looked again and noticed that the hour hand and the minute hand had exchanged places between 5 and 6. What time was it in the second case?

Somu is twice as old as Ramu. After x years, Ramu's age will be four-sevenths of Somu's age. What percentage of Ramu's present age (in years) is x?

When I was $\frac{3}{5}$ th of your present age, you were $\frac{1}{3}$ rd of my present age. If my present age after $4$ years will be $40$, then after how many years will your age be $40?$

The average age of Mahesh and Deepak is $13$ years and that of Deepak and Aarati is $20$ years. If the sum of ages of Aarati and Mahesh is $36$ years, then what is Aarati's age.

The perimeter of rectangle $ABCD=40 \mathrm{cm}$. The sum of the perimeters of rectangle $AEFD$ and rectangle $BEFC$ is $20\%$ more than that of $ABCD$. The area (in ${\mathrm{cm}}^2$) of the rectangle $ABCD$ is

The sum of a two-digit and the number obtained by reversing its digits in $121$. Find the number, if its units place digit is greater than the tens place digit by $7$.

Half the perimeter of a rectangular garden, whose length is $4 \mathrm{m}$ more than its width, is $36 \mathrm{m}$. Find the dimensions of the garden.

The sum of the digits of a two-digit number is $9$. If $17$ is subtracted from the number, both the digits of the number become equal. Find the number.

Certain number of marbles were distributed equally among few boys. Had the number of boys been $2$ less, each boy would have got $3$ marbles more. Again had the number of boys been $6$ more each boy would have got $5$ marbles less. Find the number of boys and that of marbles.$$