ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

Q1 less than four times a number is . Find the number.

Let the number

Q2 If be added to four times a certain number, the result is less than five times the number. Find the number

Let the number

Q3 Of a number is less than the original number. Find the original number.

Let the original number

Q.4 A number is more than its part. Find the number.

Let the number

Q**.**5 A number is as much greater than as is less than . Find the number.

Let the number

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

Let the number

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

Let the number

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

Let the number

Q.9 A number when divided by is diminished by . Find the number.

Let the number

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

Let the number

or

or

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

Let the two numbers be and

Therefore

Solving

Hence,

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

Let the three numbers be

Therefore,

Solving,

Therefore

The three numbers are

Q.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.

Let the two numbers be and

Given,

solving,

From

Substituting in ii)

or

Two numbers are and

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

Let the three consecutive numbers be

therefore,

Therefore the three numbers are

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

Let the two parts be and

Therefore

Solving we get

or

The other part

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

Let the two parts be and

Therefore

Solving

Therefore

Q.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.

Let the fraction be

Given

Therfore the fraction

Given,

Therefore fraction

Q.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.

Let the fraction be

Given

Fraction

Q.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.

Let the two digit number be

Given

or

Solving i) and ii) together.

Hence the number

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

Let the number added to each one of be

Q.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.

Let the two numbers be and

Given

Solving

Two numbers are and

Q22 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.

Let the number subtracted from the numerator

or

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

Perimeter of right angled triangle

Perpendicular sides

Hypotenuse

Therefore

Therefore length of side

Q.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.

Let the two digit number

Solving i) and ii)

Or

Therefore the number

Q.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

Find the length and the breadth of the plot.

Let the length and breadth

Given

or

Therefore

Q.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.

Let the length and breadth

or

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

Let the length breadth

Given

Or

Q.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

Let the length and breadth

Given,

Solving,

breadth

length

Q.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.

Let the man’s age

If son’s age

Two years letter

Man’s age

Son’s age

Man’s age

Q.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.

Let the son’s age

Man’s age

Son’s age

Man’s age

Man’s age

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

Let Rekha’s age

Seema’s age

given

or

Rekha’s sage

Seema’s sage

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

Let the present age of Parvati

age of son

Five years before

parvati

son

Given,

solving i) and ii)

or

Son’s age

Q.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?

Man’s age

Son’s age

Let in , man would be twice the age of son

or

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

Let the current age of the girl

Given,

Q.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 .

Let the distance covered at

Let the distance covered at

Total distance

Solving

or

Q.36 A motorist travelled 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.

Let the distance between town A and B

Therefore

or

Q.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

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

Q.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.

Let the speed of boat

Speed of stream

Speed of boat upstream

Speaad of the boat downstream

Therefore

Or

Q.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.

Let the base

Sides

Perimeter

Threfore

or

Base , Sides

Q.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.

Let the number of candidates

No.of candidates

Q.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?

Let money with Kamal

Then money with Raman

Or

Kamal has And Raman

Q.42 The angles of triangle are in ratio . Find the angles.

Ratio of angle

Therefore

Therefore angle are degrees.

Q.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?

Let men finish work in

Total work

Total work

Therefore

Original no of men

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

Let the two parts

Solving we get

Q.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 das did he remain absent?

Salary

Fine

Let be the number of days worked

Therefore

Or days.

ICSE Board: Suggested Books ICSE Board: Foundation Mathematics Class 8: Reference Books Class 8: NTSE Preparation --------------------------------------------------------------

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