## Thursday, 14 November 2019

### Equation in one variable (Practice Set 12.2)

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 1st 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 2nd 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