## PRACTICAL PROBLEMS IN ALGEBRA

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.

## Solving Word Problems in 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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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

Solution

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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WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 