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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useful
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).