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 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
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
$latex+ $
$latex+ $
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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