Question 1: less than four times a number is . Find the number.

Answer:

Let the number

Question 2: If be added to four times a certain number, the result is less than five times the number. Find the number.

Answer:

Let the number

Question 3: Of a number is less than the original number. Find the original number.

Answer:

Let the original number

Question 4: A number is more than its part. Find the number.

Answer:

Let the number

Question 5: A number is as much greater than as is less than . Find the number.

Answer:

Let the number

Question 6: 6 more than one-fourth of the number is two-fifth of the number. Find the number.

Answer:

Let the number

Question 7: One-third of a number exceeds one-fourth of the number by . Find the number.

Answer:

Let the number

Question 8: If one-fifth of a number decreased by is , find the number.

Answer:

Let the number

Question 9: A number when divided by is diminished by . Find the number.

Answer:

Let the number

Question 10: Four-fifths of a number exceeds two-third of the number by . Find the number.

Answer:

Let the number

or

or

Question 11: Two numbers are in the ratio and their sum is . Find the number.

Answer:

Let the two numbers be and

Therefore

Solving

Hence,

Question 12: Three numbers are in ratio and their sum is . Find the numbers.

Answer:

Let the three numbers be

Therefore,

Solving,

Therefore

The three numbers are

Question 13: Two numbers are in the ratio . If each is increased by , then ratio between the new numbers so formed is , Find the original numbers.

Answer:

Let the two numbers be and

Given,

solving,

From

Substituting in ii)

or

Two numbers are and

Question 14: The sum of three consecutive odd numbers is . Find the numbers.

Answer:

Let the three consecutive numbers be

therefore,

Therefore, the three numbers are

Question 15: Divide into two parts such that times the first part added to times the second part makes .

Answer:

Let the two parts be and

Therefore

Solving we get

or

The other part

Question 16: Divide into two parts such that the first part is less than twice the second part.

Answer:

Let the two parts be and

Therefore

Solving

Therefore

Question 17: The denominator of the fraction is more than its numerator. On subtracting from each numerator and denominator the fraction becomes. Find the original fraction.

Answer:

Let the fraction be

Given

Therefore, the fraction

Given,

Therefore fraction

Question 18: The denominator of the fraction is more than the double the numerator. On adding to the numerator and subtracting from denominator, we obtain . Find the original fraction.

Answer:

Let the fraction be

Given

Fraction

Question 19: The sum of the digits of a two-digit number is . On adding to the number, its digits are reversed. Find the original number.

Answer:

Let the two digit number be

Given

or

Solving i) and ii) together.

Hence the number

Question 20: What same numbers should be added to each one of the number to obtain numbers which are in proportion?

Answer:

Let the number added to each one of be

Question 21: The sum of two numbers is . One-fifth of the larger number is more than one-ninth of the smaller number. Find the numbers.

Answer:

Let the two numbers be and

Given

Solving

Two numbers are and

Question 22: A number is subtracted from the numerator of the fraction and six times that number is added to the denominator. If the new fraction is then find the number.

Answer:

Let the number subtracted from the numerator

or

Question 23: A right angled triangle having perimeter has its two-side perpendicular side in the ratio . Find the lengths of its sides.

Answer:

Perimeter of right angled triangle

Perpendicular sides

Hypotenuse

Therefore

Therefore, length of side

Question 24: The sum of the digits of a two-digit number is . If is added to the number formed by reversing the digits, then the result is thrice the original number. Find the original number.

Answer:

Let the two-digit number

Solving i) and ii)

Or

Therefore, the number

Question 25: The lengths of a rectangle plot of land exceeds its breadth by if the length is decreased by . and the breadth is increased by . the area is reduced by .

Answer:

Find the length and the breadth of the plot.

Let the length and breadth

Given

or

Therefore

Question 26: The length of the rectangular park is twice its breadth. If the perimeter of the park is 186 m, find its length and breadth.

Answer:

Let the length and breadth

or

Question 27: The length of the rectangle is more than its breadth. If the perimeter of the rectangle is , find its length and breadth.

Answer:

Let the length breadth

Given

Or

Question 28: The length of a rectangle is less than twice its breadth. If the length is decreased by and breadth increased by , the perimeter of the resulting rectangle is . find the length and the breadth of the original rectangle.

Answer:

Let the length and breadth

Given,

Solving,

breadth

length

Question 29: A man is five times as old as his son. In two years’ time, he will be four times as old as his son. Find their present ages.

Answer:

Let the man’s age

If son’s age

Two years letter

Man’s age

Son’s age

Man’s age

Question 30: A man is twice as old as his son. Twelve years ago, the man was thrice as old as his son. Find their present ages.

Answer:

Let the son’s age

Man’s age

Son’s age

Man’s age

Man’s age

Question 31: Seema is elder than Rekha. The ratio of their ages is . Find their ages.

Answer:

Let Rekha’s age

Seema’s age

given

or

Rekha’s sage

Seema’s sage

Question 32: ago, the age of Parvati was times the age of her son. The sum of their present ages is . Find Parvati’s age.

Answer:

Let the present age of Parvati

age of son

Five years before

Parvati

son

Given,

solving i) and ii)

or Parvati’s age

Son’s age

Question 33: A man is years old and his son is years old. In how many years, the father will be twice as old as his son at that time?

Answer:

Man’s age

Son’s age

Let in , man would be twice the age of son

or

Question 34: 9 years hence, a girl will be times as old as she was years ago. How old is she now?

Answer:

Let the current age of the girl

Given,

Question 35: A man made a trip of in hours. Some part of trip was covered at and the remaining at . find the part of the trip covered by him at .

Answer:

Let the distance covered at

Let the distance covered at

Total distance

Solving

or

Question 36: A motorist traveled from town to town at an average speed of . on his return journey, his average speed was . if the total time taken is , find the distance between the two towns.

Answer:

Let the distance between town A and B

Therefore

or

Question 37: The distance between two stations is . two motor-cyclist start simultaneously from these stations and move towards each other. The speed of one of them is faster than that of other. If the distance between them after is , find the speed of each motor-cycle

Answer:

Distance

Let the speed of 1^{st} cyclist

Then speed of 2^{nd} cyclist

Distance covered by 1s cyclist in 2hr

Distance covered by 2^{nd} cyclist in 2 hr

Therefore

Speed of 1st cyclist

Speed of 2nd cyclist

Question 38: A boat travels upstream in river in the same period of time as it travels downstream. If the ratio of stream be , find the speed of the boat in still water.

Answer:

Let the speed of boat

Speed of stream

Speed of boat upstream

Speed of the boat downstream

Therefore

Or

Question 39: The length of each of the equal sides of an isosceles triangle is longer than the base. If the perimeter of the triangle is , find the lengths of the sides of the triangle.

Answer:

Let the base

Sides

Perimeter

Therefore

or

Base , Sides

Question 40: A certain number of candidates appeared for an examination in which one-fifth of the whole plus secured first division, one-fourth plus secured second division and one-fourth minus secured third division, if the remaining candidates failed, find the total number of candidates appeared.

Answer:

Let the number of candidates

No. of candidates

Question 41: Raman has times as much money as Kamal. If Raman gives to Kamal, then Kamal will have twice as much as left with Raman. How much had each originally?

Answer:

Let money with Kamal

Then money with Raman

Or

Kamal has And Raman

Question 42: The angles of triangle are in ratio . Find the angles.

Answer:

Ratio of angle

Therefore

Therefore, angles are degrees.

Question 43: A certain number man can finish a piece of work in days. If there are more men, the work can be completed days earlier. How many men were originally there?

Answer:

Let men finish work in

Total work

Total work

Therefore

Original no of men

Question 44: Divide in two parts such that of one exceeds of the other by .

Answer:

Let the two parts

Solving we get

Question 45: A workman is paid for each day he works and is fined for each day he is absent. In a month of days he earned . For how many days did he remain absent?

Answer:

Salary

Fine

Let be the number of days worked

Therefore

Or days.

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