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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