Page 169 - ICSE Math 8

fi 3x = 2(50 – x) = 100 – 2x
fi 3x + 2x = 100 fi 5x = 100 (Transposing 2x to LHS)
5x 100
fi = fi x = 20 (Dividing both sides by 5)
5 5
So, the two numbers are 20 and (50 – 20), i.e., 20 and 30.

Example 10: A 2-digit number is such that the sum of its digits is 4. If 18 is added to the number, its digits
are reversed. Find the number.
Solution: Let the digit at the units place be x.

Then, the digit at the tens place = 4 – x
So, the number = 10 × (digit at the tens place) + (digit at the units place)
= 10 × (4 – x) + x = 40 – 10x + x = 40 – 9x
On reversing the digits, the new number = 10 × x + (4 – x) = 10x + 4 – x = 9x + 4
According to the question, Original number + 18 = New number
fi 40 – 9x + 18 = 9x + 4 fi 58 – 9x = 9x + 4 (Transposing 9x to LHS and 58 to RHS)
fi –9x – 9x = 4 – 58 fi –18x = –54 fi 18x = 54

18x 54
fi = fi x = 3 (Dividing both sides by 18)
18 18
\ Digit at the units place = 3 and digit at the tens place = 4 – 3 = 1
So, the number is 10 × 1 + 3 = 10 + 3 = 13.

Example 11: Lakshmi is a cashier in a bank. She has
currency notes of denominations of ` 100, ` 50 Try These
and ` 10 respectively. The ratio of the number 1. The denominator of a fraction is 6 more
of these notes is 2 : 3 : 5. The total cash with than its numerator. If 2 is added to both
Lakshmi is ` 4,00,000. How many notes of each the numerator and the denominator, the
denomination does she have ? fraction becomes 1 . Find the fraction.
Solution: Let the number of three notes be 2x, 3x and 5x 2
respectively. 2. Five years ago, Shikha was thrice as old as
Honey. 10 years later, Shikha will be twice
Total amount of ` 100 = 100 × 2x = 200x as old as Honey. How old are they now?
Total amount of ` 50 = 50 × 3x = 150x
Total amount of ` 10 = 10 × 5x = 50x

According to the question, 200x + 150x + 50x = 4,00,000
400x 400 000, ,
fi 400x = 4,00,000 fi = (Dividing both sides by 400)
fi x = 1,000 400 400

\ 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 12: 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

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