Practice Set 12.2

1)
Mother is 25 years older
than her son. Find son’s age, if after

8years the ratio of son’s age to mother’s
age will be 4/9.

è (Here
we have an idea about mother’s age that she is 25 years older

then her son, but
we don’t have any idea about her son’s age)

So
Let the son’s present age be x
year’s.

Mother
is 25 years older than her son (x
+ 25) years

After
8 years son’s age
to mother’s age will be
4/9

Son’s
age = (x + 8)

Mother’s
age = (x + 25 + 8) = (x + 33)

x + 8 = 4

x + 33 9

(x + 8) X 9 = (x + 33) X 4

9x
+ 72 = 4x + 132 = 9x = 4x + 132 – 72

9x = 4x + 60
= 9x – 4x = 60 = 5x = 60
= x = 60/5

x = 12

Therefore
son’s age is 12 years

2) The
denominator of a
fraction is greater than its numerator by 12.

If the
numerator is decreased by 2 and the denominator increased by 7, the new
fraction is equivalent to ½. Find the fraction.

è (Here
we have information about denominator that its greater than

numerator by 12,
but we don’t have any information about numerator, So )

Let
the numerator of the
fraction be x

Therefore
the denominator is
greater than the numerator by 12 (x + 12)

The
fraction is x /x + 12

The
numerator is decreased by 2 = x – 2

The
denominator is increased by 7 = x + 12 + 7
= x + 19

x
– 2/x + 19 = 1/2

(x – 2)
2 = (x + 19)1 i.e
2x – 4 = x + 19 i.e 2x –x = 19 +4

x = 23

So (x +
12) = 23 + 12 = 35

Therefore
fraction is 23/35

3) The
ratio of the weights of copper and zinc in brass (alloy) is 13:7. Find the
weight of zinc in a brass utensil weighing 700gm.

è Let
the ratio be x

Therefore
weight of copper be 13x and that of zinc be 7x

13x + 7x
= 700 i.e 20x = 700
i.e x = 700/20 i.e x = 35

Therefore
the weight of zinc is 7x =7 X 35 = 245gm

4)
Find 3 consecutive whole
numbers whose sum is more than 45 but

less than 54

è (whole
numbers start from 0,1,2,3…..)

Let the 3 consecutive whole numbers be x, x + 1 and x + 2

According to the 1

^{st}condition, the sum of the whole number is more
than 45

x + x + 1 + x + 2 > 45

3x + 3 > 45 i.e
3x > 45 – 3 i.e 3x > 42
i.e x > 42/3

x >
14 i.e x = 15 (x + 1) = 15 + 1 =16 (x + 2)= 15 + 2 = 17

According to the 2

^{nd}condition, the sum of the whole number is less than 54
x + x + 1 + x + 2 < 54

3x + 3 < 54 i.e
3x < 54 -3 i.e 3x < 51 i.e x < 51/3

x <
17

x = 16 (x + 1) 16 +1 = 17 (x + 2) 16 + 2= 18

5) In
a two-digit number, the digit at the tens place is twice the digit

at units place. If the number
obtained by interchanging the digits is

added to the original number, the sum
is 66. Find the original number.

è Let
the digit in units place be x

the digit at the tens place is twice the
digit at units place.

The digit at the tens place is 2x

10 X 2x + x =20x + x = 21x à 1

the number obtained by interchanging the
digits

then the digit in the unit place will be 2x
and that of tens place will

be x

10 X x + 2x = 10x +2x = 12x à 2

From the condition, the sum is 66

From 1 and 2

21x + 12x = 66 i.e
33x = 66 i.e x = 66/33 i.e x = 2

The digit in unit place is 2 and that of tens
place is 2x (2 X 2) =4

The two-digit number is 42

6) Some
tickets of 200Rs and some of 100Rs, of a drama, were sold

at a theatre. The
number of tickets of 200Rs sold was 20 more

than the number of tickets of
100Rs. The total amount received by

the theatre, by sale of tickets, was 37000
Rs. Find the number of

100Rs tickets sold.

è

Let the number of 100 Rs tickets be x

The number of tickets of 200Rs sold was 20 more
than the number

of tickets of 100Rs

Therefore 200Rs tickets (x +
20)

The total amount received was 37,000Rs

100x +200(x + 20) = 37000 i.e
100x + 200x +4000 = 37000

300x +4000 =37000 i.e
300x = 37000 -4000

i.e
300x = 33000 i.e x = 33000/300
i.e x =110

Therefore 100 Rs tickets sold were 110

7) Of three consecutive natural numbers, five times the
smallest

number is 9 more than four times the greatest number, find the

numbers.

-> Let the three consecutive number be x , x+1,and x+2

x is smallest number and x+2 is greatest number

5 times smallest number = 5x

4 times greatest number = 4(x+2)

5x=4(x+2)+9 i.e 5x=
4x+8+9 i.e 5x= 4x+17 i.e 5x-4x =17

x= 17

x+1 = 17+1 = 18

x+2 = 17 + 2 = 19

8) Raju sold a bicycle to Amit at 8% profit. Amit repaired it

spending Rs 54. Then he sold the bicycle to Nikhil for Rs 1134

with no loss no
profit. Find the cost price of the bicycle for which

Raju purchased it for.

9)
A cricketer scored 180 runs in the first match and 257 runs in

the second match. Find the number of runs he should score in the

third match, so that the average of runs in three matches be 230

the second match. Find the number of runs he should score in the

third match, so that the average of runs in three matches be 230

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