M L Aggarwal Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 3: Exercise 3.3

Form the pair of linear equations for each of the following problems and find their solution by substitution method:

The difference between two numbers is $26$. If one number is thrice the other, find the numbers.

Form the pair of linear equations for each of the following problems and find their solution by substitution method:

Two numbers are in the ratio $4:7$. If thrice the larger be added to twice the smaller, the sum is $59$. Find the numbers.

Form the pair of linear equations for each of the following problems and find their solution by substitution method:

In a basketball game, Mohan scored $4$ more than twice as many points as Rohan. If one of them had scored $2$ more points, their total would have been $60$. How many points did each score?

Form the pair of linear equations for each of the following problems and find their solution by substitution method:

A man has certain notes of denominations $20$ and $5$ which amount to $₹380$. If the number of notes of each kind are interchanged, they amount to $₹60$ less as before. Find the number of notes of each denomination.

Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

One says, "Give me a hundred, friend! I shall then become twice as rich as you" the other replies, "If you give me ten, I should be six times as rich as you." Tell me what is the amount of their (respective) capitals?

Once a mule and a donkey were talking. The mule said, "I am carrying more sacks than you. In fact, if you give me one of your sacks, then I would have twice as many as you. If I give a sack, our loads would be equal." How many sacks was each animal carrying?

The sum of the numerator and denominator of a fraction is $3$ less than twice the denominator. If the numerator and denominator are decreased by $1$, the numerator becomes half the denominator. Determine the fraction.