WORD PROBLEMS RELATED TO
LINEAR EQUATIONS
CLASS 7TH, 8TH, 9TH & 10TH
Q.1) Tarun ‘s present age is three times the present age of his sister Taru. Five years from now, he will be twice the age of his sister. Find their present ages.
SOLUTIONs :
Let the age of Taru be x years.
So, Tarun’s present age will be 3x years.
Five years hence,
Taru’ age = (x +5 ) years
Tarun’s age = (3x +5) years.
According to the problem,
3x + 5 = 2 (x + 5)
3x + 5 = 2x + 10
3x -2x = 10 -5
x = 5
Thus, Taru’s age is x =5 years.
Tarun’s age 3x = 3 * 5 = 15 years.
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Q.2) The sum of the digits of a two digit number is 10. The number formed by interchanging the digits is 36 less than the original number. Find the original number.
SOLUTION : Step –1)
Let the digit in the ten’s place be x
So, the digit in the one’s place is 10 -x
i.e. T O
(x) (10-x)
Thus, the original number = 10x +(10 – x ) =( 9x + 10)
Step —-2)
The interchanged digits are
in the ten’ place = (10 – x )
in the one’s place = x
i.e. T 0
(10 – x ) x
Thus, the interchanged number = 10 ( 10 – x ) + x
= 100 – 10x + x
= 100 – 9x
According to the problem,
Interchanged number = Original number – 36
100 -9x = (9x + 10) -36
100 – 9x= 9x + 10 – 36
100 – 9x = 9x -26
100 + 26 = 9x + 9x
126 = 18x
126 /18 = x x= 7
Thus, the digit in the ten’s place is 7 and in the one’s place is 10 -7 = 3.
So, the original number is 73.
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Q.3) On Raghav’s birthday, his mother made gulab jamuns. Raghav distributed half of the gulab jamuns among his friends. His brother took one-third of the remaining and distributed among his friends, Six gulab jamuns were given to their neighbour. Now two gulab jamuns are still remaining. Find the total number of gulab jamuns Raghav’s mother made.
SOLUTION:
Let the total number of gulab jamuns Raghav’s mother made be x
Raghav distributed half of it to friends = 1x/2
Remaining no of it = x – 1x/2 = x/2
Raghav’s brother distributed 1/3 of the remaining to friends = 1/3 ( x/2) = x/6
Number of gulab jamuns still left = 2
Number of it given to neighbour =6
According to the problem,
x/2 + x/6 + 6 +2 =x
x/2 + x/6 + 8 =x
L.C.M. OF 2 and 6 = 6
3x/6 + x/6 + 48/6 = 6x/6
3x + x + 48 = 6x
4x + 48 = 6x
48 = 6x – 4x
48 = 2x
48/2 = x x = 24
Thus, the total number of gulab jamuns Raghav’s mother made is 24
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Q.4) The ratio of Sakshi’s age to Seema’s age is 3:2 . Five years from now, the ratio of their ages will be 7:5. Find their present age.
SOLUTION :
Let Sakshi’s age be 3x years and Seema’s age be 2x years
After 5 years, Sakshi’s age = (3x + 5)years.
Seema’s age = ( 2x + 5 ) years
According to the problem,
3x + 5 / 2x + 5 = 7/5
5 ( 3x + 5 ) = 7 ( 2x + 5 )
15x 25 = 14x + 35
15x – 14x = 35 – 25 x = 10
Thus , Sakshi’s age is 3x = 3 * 10 = 30 years
Seema’s age 2x = 2*10 = 20 years
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Q.5) The numerator of a rational number is greater than it’s denominator by 5. If the numerator is decreased by 8 and the denominator is increased by 7, the new number obtained is 3/5. Find the number.
SOLUTION :
Let the denominator be = x So, the numerator = ( x + 5) So, original rational no. = x+5 /x
The new denominator = x + 7 and the new numerator = (x+5-8) = ( x- 3)
The new rational number will be ( x-3 /(x + 7 )
But given as 3/5
According to the problem,
( x-3 ) /(x + 7) = 3/5
5(x – 3) = 3 ( x + 7 )
5x -15 = 3x + 21
5x – 3x = 21 + 15
2x = 36
x = 36 / 2
x = 18
The original number is x +5 / x = 18 + 5/18 = 23 /18
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