Page 144 - Start Up Mathematics_8 (Non CCE)

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
fi –9x – 9x = 4 – 58 (Transposing 9x to LHS and 58 to RHS)

fi –18x = –54 fi 18x = 54
18x 54
fi = (Dividing both sides by 18)
18 18
fi x = 3
\ 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 13: The denominator of a fraction is 6 more than its numerator. If 2 is added to both the numerator
1
and the denominator, the fraction becomes . Find the fraction.
Solution: Let the numerator of the fraction be x. 2
Then the denominator of the fraction = x + 6
x
So, the fraction =
x + 6
If 2 is added to both the numerator and the denominator,
New numerator = x + 2 and new denominator = x + 6 + 2 = x + 8

x + 2
New fraction =
x +8

x + 2 1
According to the question, x +8 = 2 (Cross-multiply)
fi 2(x + 2) = 1(x + 8)
fi 2x + 4 = x + 8
fi 2x – x = 8 – 4 (Transposing x to LHS and 4 to RHS)

fi x = 4
\ Numerator = 4 Denominator = 4 + 6 = 10
4
\ The fraction is .
10
Example 14: Lakshmi is a cashier in a bank. She has currency notes of denominations of ` 100, ` 50 and ` 10
respectively. The ratio of the number of these notes is 2 : 3 : 5. The total cash with Lakshmi
is ` 4,00,000. How many notes of each denomination does she have ? (NCERT)
Solution: Let the number of three notes be 2x, 3x and 5x respectively.
Total amount of ` 100 = 100 × 2x = 200x
Total amount of ` 50 = 50 × 3x = 150x

Total amount of ` 10 = 10 × 5x = 50x
According to the question, 200x + 150x + 50x = 4,00,000
fi 400x = 4,00,000

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