# Equations : 10 Expected Questions for Exams

#### Ques 1.

If one number is thrice the other and their sum is 16, find the numbers.
Ans 1. Let the numbers be x  and y where x > y.
x + y = 16  and  x = 3y
putting  x  = 3y in the first equation we have :
4y = 16     y =4  and   x = 3y = 12
∴ Numbers are 12 and 4.

#### Ques 2.

A positive number when decreased by 6 is equal to 16 times the reciprocal of itself .Find the number.
Ans 2. Let the number be x.
∴  x - 6 = 16/x
or x2 - 6x - 16 =0      or   x2 - 8x + 2x  -16 = 0
or x (x - 8) + 2 ( x - 8) = 0    ( x+ 2) ( x -8) = 0
∴  x = -2  or 8.

#### Ques 3.

A number is as much greater than 28 as is less than 54. Find the number.
Ans 3. Let the number be x .
∴   x - 28 = 54 - x       or     2x  =  54 + 28  = 82           x = 41
Hence, the number is 41.

#### Ques 4.

If a number is subtracted from the square of its one -third , the result is 4. Find the square-root of the number.
Ans 4.  Let the number be x.

#### Ques 5.

The sum of the squares of three positive consecutive is 371.Find the number.
Ans 5.Let the number be x.
∴  x2/9   - x = 4    or    x2 - 9x - 36 = 0   or   x2 - 12x + 3x - 36  = 0
or  x ( x - 12) + 3 ( x - 12) = 0          ( x - 12) (x + 3) = 0
∴  x = 12 or -3
The number cannot be - ve, as its square root has to be found .So the possible value of x is 12.

#### Ques 6.

The difference of two numbers is 40% of the larger number. if the smaller number is 18. Find the sum of the number.
Ans 6.  Let the lager number be x.

#### Ques 7.

Three number are in the ratio of 2 : 3 : 4 and their product is 1536 .Find the smallest of these numbers.
Ans 7.  Let the G.C.F of the number be x.
∴ The number would bs 2x;3x and 4x.

#### Ques 8.

A number consists of two digit whose sum is 9. If 27 is added to the number, the digits are interchanged.Find the number .
Ans 8.  Let the digit of the number be x , y where y is in the unit's place and x is in the ten's place.
∴  Value of the number = 10x + y
Now, x + y = 9  and 10x + y + 27 = 10y + x
From 2nd  eqaution : 9x-9y  = - 27     or  y - x = 3     y = x + 3
Substituting the value of y in the first equation we have : x + x + 3  =9   x =3
∴  y = 3 + 3 = 6
Hence, the given number is 10 x 3 +6 =  36.

#### Ques 9.

The ratio of a two digit number and the sum of its digits is 8 :1.If the digit in the unit's place is 5 less than the digit in the ten's place, Find the number .
Ans 9. Let the digit in the ten's place be x.
Digit in the unit's place  = x -5
The value of the number  = 10x + x - 5 = 11x -5

#### Ques 10.

3 chairs and 2 tables cost Rs 700 and 5 chairs and 3 table cost Rs. 1100. What is the cost of 2 chairs and 2 tables ?
Ans 10. Let the cost of one be Rs x and that of one table be Rs y.

#### Ques 11.

The average of three numbers is 9. The numbers are such that sum of twice the first and thrice the third is 46 and thrice the first and twice the second is 42. Find the numbers .
Ans 11.

#### Ques 12.

A fraction becomes 1/2 when 4 is added to its denominator.It becomes 3/4 when 2 is subtracted from its numerator and denominator both. Find the fraction.
Ans 12.

#### Ques 13.

The difference between two numbers is 1332.When the larger number is divided by the smaller one,the quotient is 7 and the remainder is 12. Find the smaller number.
Ans 13.Let the samller number be x. Then the larger number would be 1332 + x.
Now, 1332 + x  = 7x + 12
∴  x = 220.
Hence, the smaller number is 220.

#### Ques 14.

Sohan is three as old as his son. Five years later, he shall be two and a half times as old as his son. Find Sohan's and his son's present ages.'
Ans 14. Let the  son's present age be x years.

#### Ques 15.

Six years ago, The ratio of ages of kamal and Suresh was 6:5 .Four years hence, The ratio of their ages will be 11:10. What is Suresh's age at present ?
Ans 15. Let the present ages of kamal and suresh be denoted by K and S respectively.'

#### Ques 16.

The average age of an adult in a class is 38 years. If twelve new students with an average age of 30 years are included , the average age decreases by 4 years. Find the original strength of the class.
Ans 16. Let the original number if students in the class be x.
. . 38x  + 30 x 12 = ( 38 -4 ) ( x + 12)
or     38x  + 360  = 34x + 408  or 4x = 48   ⇒  x = 12
Hence, the original strength of the class = 12.

#### Ques 17.

The ratio of kapil's age to kirti ' age is 3:5 and the sum of their ages is 80 years . what will be the ratio of their ages after 10 years?
Ans 17. Let the G.C.F. of Kapil's and kirti's age be x.

#### Ques 18.

Mr. Subramaniam had Rs 240 in one -Rupee, 5 rupee and 10 rupee notes. If he has equal number of notes of all denominations, find the total number of notes he has.
Ans 18. Let the number of notes of each denominator be x.