Q. 34.3( 296 Votes )

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

(i) The difference between two numbers is 26 and one number is three times the other. Find them.

(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.

(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of25 km?

(v) A fraction becomes if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes Find the fraction.

(vi) 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?

Answer :

i) Let larger number = x

Let smaller number = y


According to the question,


=


=


And,


=


Comparing values of x from both equation, we get,





So, x = 3y = 3 × 13 = 39


Hence, the numbers are 13 and 39.


ii) Let the first angle = x


Let second angle = y


According to the question,


=


x =


And,


=


Putting value of x from equation (i) to (ii). we get,


=


=


=


so,


Hence the angles are 99ᵒ and 81ᵒ


iii) Let cost of each bat = Rs. X


Let cost of each ball = Rs. Y


According to the question,


=


=


=


And,


=


Putting value of y from Equation (i) to equation (ii)


=


=


=


=


Putting value of x in equation (i) , we get


=


Hence,


Cost of each bat = Rs.500 and Cost of each ball = Rs. 50


iv) Let the fixed charge for taxi = Rs. X


Let variable cost per km = Rs. y


We know that,


Total cost = Fixed charge + Variable Charge


According to the question,


=


=


And, For a journey of 15 km charge paid = Rs.155


so,


Putting value of x from equation (i) to equation (ii). we get,


=


=


=


Putting value of y in equation (i) . we get,


=


So, People have to pay for travelling a distance of 25 km


=


v) Let numerator = x


Let denominator = y


Fraction will be =


According to the question,


Fraction become


=


=


=


=


And, if 3 is added to both numerator and denominator it become


=


=


Putting value of x from equation (i) to equation (ii)


=


=


=


= y = 9


Putting value of y in equation (i)


=


Hence , the fraction is


vi) Let present age of Jacob = X years


Let present age of his son = Y years


Five year hence,


Age of Jacob = X + 5


Age of son = Y + 5


And, age of Jacob is 3 times of his son Given


=


=


=


Five years ago,


Age of Jacob = X - 5


Age of son = Y - 5


And, Jacob's age was 7 times of his son Given


=


=


=


Putting value of X from equation (i) to equation (ii)


=


=


=


Putting value of Y in (i)


=


Hence,

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