SIMPLE PRACTICE WORKSHEETS
RELATED TO LINEAR EQUATIONS
CLASS 5TH, 6TH & 7TH
STEP BY STEP EASY SOLUTION —WORKSHEET–2
Q.1) Find two numbers such that one of them is five times the other and their difference is 132.
SOLUTION :
Let the smaller number be = x
hence, the greater number is = 5x
According to the question,
5x – x = 132
4x = 132 x = 132 /4
x = 33
Thus, the smaller number is 33 and the greater number is 5x = 5 * 33 = 165
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Q.2) The sum of two consecutive even numbers is 74. Find the numbers.
SOLUTION :
Let the first consecutive even number be = x
and the second consecutive number = x + 2
According to the question,
x + ( x+ 2) = 74
x + x + 2 = 74
2x = 74 – 2
2x = 72
x = 72 /2
x = 36
Thus, the first consecutive number is x = 36
and the second consecutive number is x + 2 = 36 + 2 = 38
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Q.3) The sum of three consecutive odd numbers is 21. Find the numbers.
SOLUTION :
Let the first consecutive odd number be = x
So, the second consecutive odd number =( x + 2)
and the third consecutive odd number = (x + 4)
According to the question,
x + ( x + 2)+ (x + 4 ) = 21
x + x + 2 + x + 4 = 21
3x + 6 = 21
3x = 21 -6
3x = 15
x = 15 /3
x = 5
Thus, the first consecutive odd number is x = 5
the second consecutive odd number = x + 2 = 5 + 2 = 7
and the third consecutive odd number = x + 4 = 5 + 4 = 9
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Q.4) Reena is 6 years older than her brother Ajay. If the sum of their ages is 28 years. what are their present age ?
SOLUTION :
Let Ajay’s present age be = x years
hence, Reena’s present age =( x +6) years
According to the question,
x + ( x + 6 ) = 28
x + x + 6 = 28
2x + 6 = 28
2x = 28 – 6
2x = 22
x = 22 / 2 x = 11
Thus, Ajay’s present age is x = 11 years and Reena’s present age = x + 6 = 11 + 6 = 17 years
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Q.5) Deepak is twice as old as his brother Vikas. If the difference of their ages be 11 years, find their present ages.
SOLUTION :
Let Vikas’ present age be = x years and Deepak’s present age = 2x years
According to the question,
2x – x = 11 x = 11 years
Thus, Vikas’ present age = x = 11 years and Deepak’s present age = 2x = 2* 11 = 22 years
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Q.6) Mrs. Goel is 27 years older than her daughter Rekha. After 8 years she will be twice as old as Rekha. Find their present ages.
SOLUTION:
Let Rekha’s present age be = x years Mrs. Goel’s present age = ( x+27 ) years
After 8 years ,
Rekha’ age = ( x + 8) years and Mrs. Goel’s age = (x + 27 ) + 8 =( x + 35) years
According to the question,
x + 35 = 2( x + 8 )
x + 35 = 2x + 16
35 – 16 = 2x – x
19 = x
Thus, Rekha’s present age = 19 years and Mrs. Goel’s present age = x + 27= 19 + 27 =46 years
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Q.7)A man is 4 times as old as his son. After 16 years he will be only twice as old as his son. Find
their present ages.
SOLUTION:
Let the son’s present age be = x years and the man’s present age = 4x years
After 16 years,
son’s age = (x+16) years and man’s age =( 4x +16) years
According to the question,
4x + 16 = 2 ( x + 16 )
4x + 16 = 2x + 32
4x – 2x = 32 -16
2x = 16 x = 16 / 2 x= 8
Thus, the son’s present age =x= 8 years and the man’s present age = 4x =4 *8 = 32 years
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