Q. 34.3( 318 Votes )

# Form the pair of

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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