Problem 1 :
The denominator of a fraction is 9/4 of the numerator. Find the fraction.
Solution :
Let x be the numerator.
Given : The denominator of the fraction is 9/4 of the numerator.
Then, the denominator is 9x/4.
Therefore, the required fraction is
= x / (9x/4)
= x ⋅ (4/9x)
= (x ⋅ 4) / 9x
= (1 ⋅ 4) / 9
= 4/9
Problem 2 :
In a school, there are 450 students in total. If 2/3 of the total strength is boys, find the number of girls in the school.
Solution :
Given : 2/3 of the total strength is boys
Then, the number of boys in the school is
= 2/3 ⋅ 450
= (2 ⋅ 450) / 3
= (2 ⋅ 150) / 1
= 300
Therefore, the number of girls in school is
= Total strength  No. of boys
= 450  300
= 150
Problem 3 :
If the fraction is multiplied 3, it becomes 5/4. And sum of the numerator and denominator is 17. Find the fraction.
Solution :
Let x/y be the required fraction.
Given : If the fraction is multiplied 3, it becomes 5/4.
Then, we have
3 ⋅ x/y = 5/4
3x/y = 5/4
12x = 5y
12x  5y = 0 (1)
Given : Sum of the numerator and denominator is 17.
x + y = 17 (2)
Solving (1) and (2), we get
x = 5 and y = 12
x/y = 5/12
So, the required fraction is 5/12.
Problem 4 :
Of two numbers, 1/5th of a the greater equal to 1/3rd of the smaller and their sum is 16. Find the numbers.
Solution :
Let x and y be the required two numbers such that x > y.
Given : 1/5th of a the greater equal to 1/3rd of the smaller.
Then, we have
x/5 = y/3
3x = 5y
3x  5y = 0 (1)
Given : Sum of the numbers is 16.
Then, we have
x + y = 16 (2)
Solving (1) and (2), we get
x = 10 and y = 6
So, the numbers are 6 and 10.
Problem 5 :
The fourth part of a number exceeds the sixth part by 4. Find the number.
Solution :
Let x be the required number.
Then,
Fourth part of the number = x/4
Sixth part of the number = x/6
Given : The fourth part of a number exceeds the sixth part by 4
Then, we have
x/4 = x/6 + 4
x/4  x/6 = 4
3x/12  2x/12 = 4
(3x  2x) / 12 = 4
x/12 = 4
x = 48
So, the number is 48.
Problem 6 :
A work was assigned to A and B. A completed 2/3 of the work and B completed 5/8 of the remaining work. What fraction of the original word completed by B ?
Solution :
Given : A completed 2/3 of the work.
Remaining = 1/3
Given : B completed 5/8 of the remaining work
Then, the part of the work completed by B is
= 5/8 ⋅ 1/3
= (5 ⋅ 1) / (8 ⋅ 3)
= 5/24
= 5/24
So, B completed 5/24 of the original work.
Problem 7 :
Rachel bought a pizza and ate 2/5 of it. If he had given 2/3 of the remaining to his friend, what fraction of the original pizza will be remaining now ?
Solution :
Given : Rachel 2/5 of a pizza.
Remaining = 3/5
Given : He gave 2/3 of the remaining to his friend.
Then, Amount of pizza given to his friend is
= 2/3 ⋅ 3/5
= (2 ⋅ 3) / (3 ⋅ 5)
= (2 ⋅ 1) / (1 ⋅ 5)
= 2/5
Now, we have
Remaining pizza
=
Total amount of pizza

(Amount of pizza eaten by Rachel + Amount of Pizza given to his friend)
Then, we have
Remaining pizza = 1  (2/5 + 2/5)
Remaining pizza = 1  4/5
Remaining pizza = 5/5  4/5
Remaining pizza = 1/5
So, 1/5 of the original pizza will be remaining.
Problem 8 :
A work was assigned to David. He completes 1/9 of the work each day. If the total work is considered to be 450 units, how many units will he complete in 5 days ?
Solution :
Given : David completes 1/9 of work each day.
Then, the fraction of work completed by him in 5 days is
= 5 ⋅ 1/9
= (5 ⋅ 1) / 9
= 5/9
Given : The total work is considered to be 450 units.
Then, the number of units completed in 5 days is
= 5/9 ⋅ 450
= (5 ⋅ 450) / 9
= (5 ⋅ 50) / 1
= 250/1
= 250
So, David will complete 250 units of work in 5 days.
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