**Practical Problems in Algebra :**

Questions have been prepared in this section will be much useful for the students who would like to take practice on the topic algebra.

**Question 1 :**

Martin is four times as old as his brother Luther at present. After 10 years he will be twice the age of his brother. Find their present ages.

(A) 10 years , 3 years

(B) 5 years , 10 years

(C) 20 years , 15 years

(D) 8 years , 4 years

**Question 2 :**

A father is 30 years older than his son and one year ago he was four times as old as his son. Find the present ages of his father and his son.

(A) 11 years , 41 years

(B) 5 years , 20 years

(C) 20 years , 65 years

(D) 8 years , 44 years

**Question 3 :**

The ages of Abraham and Adam are in the ratio 5:7. If Abraham was 9 years older and Adam 9 years younger, the age of Abraham would have been twice of Adam. Find the present ages of them.

(A) 12 years , 15 years

(B) 8 years , 15 years

(C) 15 years , 21 years

(D) 4 years , 14 years

**Question 4 :**

Liza's mother is four times a old as Liza. After five years her mother will be three times as old as she will be then. What is their present ages ?

(A) 10 years , 40 years

(B) 8 years , 32 years

(C) 5 years , 20 years

(D) 4 years , 16 years

**Question 5 :**

The sum of the present ages of kiran and Kate is 60 years. If the ratio of their present ages be 7:8, find their present age.

(A) 28 years , 32 years

(B) 30 years , 30 years

(C) 15 years , 45 years

(D) 14 years , 46 years

**Question 6 :**

Andrea is three times as old as her sister Anu. Three years ago, she was two years less than four times the age of her sister. Find their present ages.

(A) 30 years , 3 years

(B) 54 years , 18 years

(C) 33 years , 11 years

(D) 15 years , 5 years

**Question 7 :**

The sum of two numbers is 90 and they are in the ratio is 4:5. Find those numbers.

(A) 20 and 70 (B) 40 and 50

(C) 35 and 55 (D) 28 and 62

**Question 8 :**

If the same numbers is added to both the numerator and denominator of a fraction 3/5, then the result is 3/4. Find the number.

(A) 3 (B) 4 (C) 5 (D) 8

**Question 9 :**

Two numbers are such that the ratio between them is 5 : 7. When 7 is added to each of them, the ratio becomes 2 : 3. Find the numbers.

(A) 40 and 56 (B) 10 and 14

(C) -39 and -49 (D) 30 and 42

**Question 10 :**

The sum of two numbers is 135 and they are in the ratio 7 : 8 . Find those numbers.

(A) 28 and 32 (B) 35 and 40

(C) 63 and 72 (D) 42 and 56

**Question 11 :**

The difference of two numbers is 72 and the quotient obtained by dividing the one by other is 3. Find the numbers.

(A) 19 and 57 (B) 36 and 108

(C) 163 and 72 (D) 54 and 156

**Question 12 :**

In a certain fraction, the denominator is 4 less than the numerator. If the number 3 is added to both the numerator and denominator, the resulting fraction is equal to 9/7, find the original fraction.

(A) 7/9 (B) 8/19 (C) 2/21 (D) 15/11

**Question 13 :**

The sum of digits of a two digit numbers is 15 and if 9 is added to the number the digits are interchanged. Find the required number.

(A) 36 (B) 57 (C) 27 (D) 78

**Question 14 :**

The sum of the digits of a two digit number is 10. If the number formed by reversing the digits is less than the original number by 36,find the required number.

(A) 73 (B) 55 (C) 64 (D) 28

**Question 15 :**

The unit's digit of a two digit number is twice its ten's digit. If 18 is added to the number, the digits interchange their places. Find the number.

(A) 48 (B) 24 (C) 36 (D) 84

**Question 16 :**

The sum of the digits of two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.

(A) 48 (B) 75 (C) 39 (D) 84

**Question 17 :**

The number consists of two digits whose sum is 9. If 45 is added to the number, the digits are reversed. Find the number.

(A) 63 (B) 27 (C) 36 (D) 81

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