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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

Let the two numbers be and

Therefore

Solving

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

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

Given

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

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 1st cyclist

Then speed of 2nd cyclist

Distance covered by 1s cyclist in 2hr

Distance covered by 2nd 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

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 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

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Thanks a lot to provide a good fascility to help as a reference during printing mistakes in books . Devershi Samrat (Theologist, a Principal , a super teaching specialist and principaling ). Padrauna( UP).