Page 145 - Start Up Mathematics_8 (Non CCE)

400x 400 000, ,
fi = (Dividing both sides by 400)
400 400
fi x = 1,000
\ Number of ` 100 notes = 2x = 2 × 1,000 = 2,000
Number of ` 50 notes = 3x = 3 × 1,000 = 3,000

Number of ` 10 notes = 5x = 5 × 1,000 = 5,000
Example 15: Five years ago, Shikha was thrice as old as Honey. 10 years later, Shikha will be twice as old
as Honey. How old are they now?
Solution: Honey’s age 5 years ago = x years
Shikha’s age 5 years ago = 3x years
Honey’s present age = (x + 5) years
Shikha’s present age = (3x + 5) years
Honey’s age 10 years later = (x + 5) + 10 = (x + 15) years
Shikha’s age 10 years later = (3x + 5) + 10 = (3x + 15) years
According to the question, 3x + 15 = 2(x + 15)
fi 3x + 15 = 2x + 30
fi 3x – 2x = 30 – 15 (Transposing 2x to LHS and 15 to RHS)

fi x = 15
\ Honey’s present age = x + 5 = 15 + 5 = 20 years
and Shikha’s present age = 3x + 5 = 3 × 15 + 5 = 45 + 5 = 50 years
Example 16: There are 100 multiple choice questions in an examination. For every correct answer the
student gets 5 marks and for every wrong answer 2 marks are deducted from the total score
of correct answers. Suppose, the student attempts all the questions and his total score is 220,
how many questions did he attempt correctly?

Solution: Let the number of questions attempted correctly be x.
Then, the number of questions attempted incorrectly = 100 – x
According to the question, 5x – 2(100 – x) = 220
fi 5x – 200 + 2x = 220

fi 7x – 200 = 220
fi 7x = 220 + 200 = 420 (Transposing –200 to RHS)
7x 420
fi = (Dividing both sides by 7)
7 7
fi x = 60

So, the student attempted 60 questions correctly.
Example 17: The sum of two numbers is 2,170. If 2.5% of one number is equal to 4.5% of the other, find
the two numbers.
Solution: Let one of the numbers be x.
\ The other number = 2,170 – x
According to the question, 2.5% of x = 4.5% of (2,170 – x)

25. 45.
2 170 - x
fi ¥ x = ¥ (, )
100 100
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