The sum of two numbers is 1215 and their HCF is 81. If one of the numbers lies between 250 and 350 and the other lies between 800 and 900. then what is the difference between the two numbers?
The sum of two numbers is 1215 and their HCF is 81. If one of the numbers lies between 250 and 350 and the other lies between 800 and 900. then what is the difference between the two numbers? Correct Answer 567
Given:
Sum = 1215
HCF = 81
Concept used:
If we divide two number by their HCF then the quotient will be co - Prime i.e. prime to each other.
Calculation:
Let the numbers be x and y
Then, HCF(x, y) = 81
We can write the number x = 81p and y = 81q
Where p and q are the co prime number to each other.
According to the question.
⇒ x + y = 1215
⇒ 81p + 81q = 1215
⇒ p + q = 1215/81
⇒ p + q = 15
We have two condition with us now,
(p + q) is 15 and p and q are co-prime to each other
Possible pair are (1, 14), (2, 13), (4, 11), and (7, 8) both are co prime number
)1 If pairs are (1, 14) →
⇒ x = 81 × 1 = 81
⇒ y = 81 × 14 = 1134
2) If pairs are (2, 13) →
⇒ x = 81 × 2 = 162
⇒ y = 81 × 13 = 1053
3) If pairs are (4, 11) →
⇒ x = 81 × 4 = 324
⇒ y = 81 × 11 = 891
4) If pairs are (7, 8) →
⇒ x = 81 × 7 = 567
⇒ y = 81 × 8 = 648
According to question;
If one of the numbers lies between 250 and 350 and the other lies between 800 and 900.
Only pair (3) i.e (4, 11) satisfy.
So, difference of two numbers = 891 - 324 = 567
∴ The answer is 567.
