**Problems Based on Articles and their cost**

Question 4: pens and pencils together cost and pens and pencils cost . Find the cost of one pen and one pencil.

Answer:

Let the cost of a pen . and the cost of a pencil .

Therefore given:

… … … … … (i)

… … … … … (ii)

Now multiplying equation( (i) by and equation (ii) by we get

… … … … … (iii)

… … … … … (iv)

Subtracting (iv) from (iii) we get

Substituting in (i) we get

Question 5: A person has pens and pencils with together are in number.If she had more pencils and less pens, then the number of pencils would become times the number of pens. Find the number of pens and pencils that the person had.

Answer:

Let the number of pens . and the number of pencil .

Therefore given:

… … … … … (i)

… … … … … (ii)

Now multiplying equation( (i) by we get

… … … … … (iii)

Subtracting (i1) from (iii) we get

Substituting in (i) we get

Question 6: books and pens together cost whereas books and pens together cost . Find the cost of one books and two pens.

Answer:

Let the cost of a book . and the cost of a pen .

Therefore given:

… … … … … (i)

… … … … … (ii)

Now multiplying equation( (i) by and equation (ii) by we get

… … … … … (iii)

… … … … … (iv)

Subtracting (iv) from (iii) we get

Substituting in (i) we get

Question 7: On selling a TV at gain and a fridge at gain, a shopkeeper gains . But if he sells the TV at gain and the fridge at loss, he gains on the transaction. Find the actual prices of the TV and the fridge.

Answer:

Let the cost of TV . and the cost of Fridge .

Therefore given:

… … … … … (i)

… … … … … (ii)

Now multiplying equation( (i) by we get

… … … … … (iii)

Adding (iii) from (i) we get

Substituting in (i) we get

Question 8: A lending library has a fixed charge for the first three days and an additional charge for each additional day. Person A paid for a book kept for days while Person B paid for the book kept for days. Find the fixed charge and the charge for each additional day.

Answer:

Let the fixed cost . and the cost per day .

Therefore given:

… … … … … (i)

… … … … … (ii)

Subtracting (ii) from (i) we get

Substituting in (i) we get

**Problems Based on Numbers**

Question 9: The sum of the digits of a two digit number is and the difference between the number and that formed by reversing the digits is . Find the number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given: … … … … … (i)

… … … … … (ii)

Adding (i) and (ii) we get

Hence and the number is .

Question 10: The sum of two digit number and the number obtained by reversing the order of its digits is , and the two digits differ by . Find the number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given:

… … … … … (i)

Also … … … … … (ii)

Consider +ve sign

Solving and and and the number is

Consider -ve sign

Solving and and and the number is

Question 11: The sum of two digit number and the number formed by interchanging its digits is . If is subtracted from the first number, the new number is more than times the sum of the digits in the first number. Find the first number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given:

… … … … … (i)

Also … … … … … (ii)

Solving and and and the number is

Question 12: The sum of two numbers is . If their sum is times their difference, find the numbers.

Answer:

Let the two numbers be and

Therefore … … … … … (i)

… … … … … (ii)

Now multiplying equation (i) by and adding (i) and (ii) we get

Therefore we get and

Question 13: The sum of the digits of a two digit number is . The number obtained by reversing the order of the digits of the given number exceeds the given number by . Find the given number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given:

… … … … … (i)

Also … … … … … (ii)

Solving and we get and the number is

Question 14: The sum of two numbers is and the difference between their squares is . Find the numbers.

Answer:

Let the two numbers be and

Therefore … … … … … (i)

… … … … … (ii)

Adding (i) and (ii) we get

Therefore we get and

Question 15: A digit number is four times the sum of its digits. If is added to the number, the digits are reversed. Find the number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given:

… … … … … (i)

Also … … … … … (ii)

Solving and we get and the number is

Question 16: A digit number is such that the product of its digits is . If is added to the number, the digits interchange their places. Find the number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given:

… … … … … (i)

Also … … … … … (ii)

Substituting (ii) in (i) we get

(not possible)

For we get

We get and the number is

Question 17: times two digit number is equal to times the number obtained by reversing the digits. If the difference between the digits is . Find the number.

Answer:

Let the digit in unit place is and that in tenth place is .

Therefore Number

Number formed by reversing the digits

Given:

… … … … … (i)

Also … … … … … (ii)

Solving and we get and the number is

**Problems Based on Fractions**

Question 18: A fraction become if is added to both numerator and denominator. If, however, is subtracted from both numerator and denominator, the fraction becomes . What is the fraction?

Answer:

Let the fraction

Therefore based on the given conditions:

… … … … … (i)

and … … … … … (ii)

Multiplying (ii) by and subtracting it from (i) we get

Therefore .

Substituting in (i) we get

Therefore the fraction is

Question 19: A denominator of a fraction is more than twice the numerator. When both the numerator and denominator are decreased by , the denominator becomes times the numerator. Determine the fraction.

Answer:

Let the fraction

Therefore based on the given conditions:

… … … … … (i)

and … … … … … (ii)

Subtracting (ii) from (i) we get

Therefore .

Substituting in (i) we get

Therefore the fraction is

Question 20: A fraction becomes is is subtracted from both its numerator and denominator. If is added to both numerator and denominator, it becomes . Find the fraction.

Answer:

Let the fraction

Therefore based on the given conditions:

… … … … … (i)

and … … … … … (ii)

Subtracting (ii) from (i) we get

Therefore .

Substituting in (i) we get

Therefore the fraction is

Question 21: If the numerator of the fraction is multiplied by and the denominator is reduced by the fraction becomes . And if the denominator is doubled and the numerator is increased by , the fraction becomes . Determine the fraction.

Answer:

Let the fraction

Therefore based on the given conditions:

… … … … … (i)

and … … … … … (ii)

Subtracting (ii) from (i) we get

Therefore .

Substituting in (i) we get

Therefore the fraction is

Question 22: The sum of the numerator and denominator of a fraction is . If the denominator is increased by , the fraction reduces to . Find the fraction.

Answer:

Let the fraction

Therefore based on the given conditions:

… … … … … (i)

and … … … … … (ii)

Adding (i) and (i) we get

Therefore .

Substituting in (i) we get

Therefore the fraction is

Question 23: The sum of the numerator and denominator of a fraction is less than twice the denominator. If the numerator and denominator are decreased by , the numerator becomes half the denominator. Determine the fraction.

Answer:

Let the fraction

Therefore based on the given conditions:

… … … … … (i)

and … … … … … (ii)

Subtracting (ii) from (i) we get

Therefore .

Substituting in (i) we get

Therefore the fraction is