Problem 1 :
Twice a number is 500 more than six times the number. What is the number?
Solution :
Let x be the number.
2x = 6x + 500
2x - 6x = 500
-4x = 500
x = -500/4
x = -125
So, the required number is -125.
Problem 2 :
Three-sevenths of a number is 24. Find the number.
Solution :
Let x be the number.
3/7 of x = 24
(3/7) ⋅ x= 24
x = 24 (7/3)
x = 8 ⋅ 7
x = 56
So, the required number is 56.
Problem 3 :
What number increased by ¼ of itself is equal to 30?
Solution :
Let x be the required number.
x + (1/4) of x = 30
x + x/4 = 30
(4x + x)/4 = 30
5x / 4 = 30
5x = 120
x = 120/5
x = 24
So, the required number is 24.
Problem 4 :
Find a number such that ¼ of the number is 50 less than 2/3 of the number.
Solution :
Let x be the number,
1/4 of x = (2/3) of x - 50
x/4 = (2x/3) - 50
x/4 = (2x - 150)/3
Doing cross multiplication, we get
3x = 4(2x - 150)
3x = 8x - 600
3x - 8x = -600
-5x = -600
x = 600/5
x = 120
So, the required number is 120.
Problem 5 :
The denominator of a fraction exceeds the numerator of a fraction by 25. The value of the fraction is 3/8 . Find the fraction.
Solution :
Let x be the numerator.
denominator = x + 25
x/(x + 25) = 3/8
8x = 3(x + 25)
8x = 3x + 75
8x - 3x = 75
5x = 75
x = 75/5
x = 15
So, the required fraction is 15/40
Problem 6 :
If 6 times a number is decreased by 6, the result is the same as when 3 times the number is increased by 12. Find the number.
Solution :
Let x be the number,
6x - 6 = 3(x + 12)
6x - 6 = 3x + 36
6x - 3x = 36 + 6
3x = 42
x = 42/3
x = 14
So, the required number is 14.
Problem 7 :
Separate 84 into two parts such that one part will be 12 less than twice the other.
Solution :
Let x be the number. Then the other number 2x - 12
Sum of those two numbers = 84
x + 2x - 12 = 84
3x - 12 = 84
3x = 84 + 12
3x = 96
x = 96/3
x = 32
2x - 12 ==> 2(32) - 12 ==> 52
So, the required numbers are 32 and 52.
Problem 8 :
The difference between two numbers is 24. Find the numbers if their sum is 88.
Solution :
Let x and x + 24 be two numbers.
Sum of the numbers = 88
x + x + 24 = 88
2x = 88 - 24
2x = 64
x = 64/2
x = 32
x + 24 ==> 32 + 24 ==> 76
So, the required numbers are 32 and 76.
Problem 9 :
One number is 3 times another number. If 17 is added to each, the first resulting number is twice the second resulting number. Find the two numbers.
Solution :
Let x and 3x be the numbers.
x + 17 and 3x + 17
3x + 17 = 2(x + 17)
3x + 17 = 2x + 34
3x - 2x = 34 - 17
x = 17
The other number = 3x ==> 3(17) = 51
So, the two numbers are 17 and 51.
Problem 10 :
The larger of two numbers is 1 less than 3 times the smaller. If 3 times the larger is 5 more than 8 times the smaller, find the numbers.
Solution :
Let x be the smaller number
Larger number = 3x - 1
3(3x - 1) = 8x + 5
9x - 3 = 8x + 5
9x - 8x = 5 + 3
x = 8
the other number = 3x - 1==> 3(8) - 1 ==> 23
So, the required numbers are 8 and 23.
Problem 11 :
The second of three numbers is one less than the first. The third number is 5 less than twice the second. If the third number exceeds the first number by 12, find the three numbers.
Solution :
Let x be the first number.
Second number = x - 1
Third number = 2(x - 1) - 5
2x - 7 = x + 12
2x - x = 12 + 7
x = 19
x - 1 = 18
2(x - 1) - 5 = 31
So, the required numbers are 18, 19 and 31.
Problem 12 :
One number is 4 more than 5 times another number. If 6 is added to each, the first resulting number is three times the second resulting number. Find the two numbers.
Solution :
Let x be the other number
one number = 5x + 4
6 is added to each, then x + 6 and 5x + 4 + 6
5x + 10 = 3(x + 6)
5x + 10 = 3x + 18
5x - 3x = 18 - 10
2x = 8
x = 4
5x + 4 ==> 5(4) + 4
= 24
So, the required numbers are 4 and 24.
Mar 14, 24 10:44 PM
Mar 14, 24 10:12 AM
Mar 14, 24 09:52 AM