It is given that ab=24
⇒ b(b+5)=24 [Substituting a=b+5 from Eq (1)]
⇒ b(b+5)=3(3+5) ∴b=3
Substituting b=3 in Eq(1) ⇒ a=8
∴ Original number =10a+b=10×8+3=83
Answer: 83
4.3 Fraction-based questions
Example 8
The sum of the numerator and denominator of a fraction is 6. When 3 is added to each of the numerator and the denominator, the fraction's value becomes 21. What is the value of the initial fraction in decimal form?
Solution
Let the numerator and denominator of the initial fraction be a and b respectively.
Statement1: The sum of the numerator and denominator of a fraction is 6.
a+b=6 -----(1)
Statement2: When 3 is added to each of the numerator and the denominator, the fraction's value is 21
Value of initial fraction in decimal form =ba=51=0.2
Answer: 0.2
Example 9
When the numerator and denominator of a certain fraction are reduced by 2 and 1 respectively, then the fraction becomes 52. However, if the numerator and denominator of the same fraction were increased by 1 and 4 respectively, the fraction would have become 73. What is the sum of the numerator and denominator of the original fraction?
(1) 20
(2) 25
(3) 40
(4) 45
Solution
Let the numerator and denominator of the initial fraction be a and b respectively
.
Statement1: When the numerator and denominator of a certain fraction are reduced by 2 and 1 respectively, then the fraction becomes 52. b−1a−2=52 ⇒ 5a−2b=8 -----(1)
Statement2: if the numerator and denominator of the same fraction were increased by 1 and 4 respectively, the fraction would have become 73.