WORD PROBLEMS RELATED TO
LINEAR EQUATIONS
CLASS 7th, 8th, 9th AND 10th
Q.1) The ratio of the tens digit to the ones digit of a two-digit number is 2 : 3. If 27 is added to the number, the digits interchanging their places. Find the number.
SOLUTION:
Given:
Ratio of ten’s digit to one’s digit = 2 : 3
Let the digit in one’s place = 3x
Let the digit in ten’s place = 2x
STEP – 1) i.e., Ten’s Units
2x 3x
The original number = 10 ( 2x ) + 3x = 20x + 3x
= 23x
STEP – 2) If 27 is added to the number, the digit interchange their place
i.e., Ten’s Units
3x 2x
New number = 10 ( 3x ) + (2x ) = 30x + 2x
= 32x
According to the problem,
23x + 27 = 32x
27= 32x – 23x
27 = 9x
27 / 9 = x
3 = x
Hence, Ten’s digit = 2x = 2 * 3 = 6
One’s digit = 3x = 3 * 3 = 9
Therefore, 6 and 9 are the required numbers.
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Q.2) If 7 is subtracted from five times a number, the difference is 8 more than twice the number. Find the number.
SOLUTION:
Given:
Let the number = x
7 subtracted from 5 times a number
( 5x – 7 ) —- Equation – 1)
8 more than twice the number
( 2x + 8 ) —- Equation – 2)
According to the problem,
( 5x – 7 ) = 2x + 8
5x – 2x = 8 + 7
3x = 15
x = 15 / 3
x = 5
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Q.3) Four years ago, my father’s age was five times my age. At present the sum of our ages is 50. What is my father’s present age ?
SOLUTON:
Given:
Let my present age = x years
Let my father’s present age = ( 50 – x ) years
4 years ago,
My age = ( x – 4 ) years
My father’s age = ( 50 – x ) – 4
= ( 46 – x )
According to the problem,
( 46 – x ) = 5 ( x – 4 )
46 – x = 5x – 20
46 + 20 = 5x + x
66 = 6x
66 / 6 = x
11 = x
Hence, this is my present age = x = 11 years
This is my father’s present age = 50 – x
= 50 – 11
= 39 years
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Q.4) Arpit has Rs. 100, Rs. 50 and Rs. 10 notes in his wallet in the ratio 2 : 3 : 5. Find the total amount of money in his wallet if he has a total of 50 notes of all the three denominations.
SOLUTION:
Given:
Each note of Rs. 100 denomination = 2x
Total amount of Rs. 100 denomination = Rs. 200x
Each note of Rs. 50 denomination = 3x
Total amount of Rs. 50 denomination = Rs. 150x
Each note of Rs. 10 denomination = 5x
Total amount of Rs. 10 denomination = Rs. 50x
Total notes = 50 notes
2x + 3x + 5x = 50
10x = 50
x = 50 / 10
x = 5
Total amount = 200x + 150x + 50x
= 200 ( 5 ) + 150 ( 5 ) + 50 ( 5 )
= 1000 + 750 + 250
= Rs. 2000
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