Question : The sum of the two numbers is 1215 and their HCF is 81. If the numbers lie between 500 and 700, then the sum of the reciprocals of the numbers is _____.
Option 1: $\frac{5}{702}$
Option 2: $\frac{5}{378}$
Option 3: $\frac{5}{1512}$
Option 4: $\frac{5}{1188}$
Correct Answer: $\frac{5}{1512}$
Solution : Let the number be 81$x$ and 81$y$ 81$x$ + 81$y$ = 1215 ⇒ $x + y = \frac{1215}{81}$ = 15 Pair of $x+ y$ = (1,14), (2,13), (4,11), and (7,8) ⇒ $x = 7$ and $y = 8$ First number = 81 × 7 = 567 Second number = 81 × 8 = 648 The sum of reciprocals = $\frac{1}{81x}$ + $\frac{1}{81y}$ = $\frac{1}{567}$ + $\frac{1}{648}$ = $\frac{1}{81}$[$\frac{1}{7}$ + $\frac{1}{8}$] = $\frac{1}{81}$ × $\frac{15}{56}$ = $\frac{5}{1512}$ Hence, the correct answer is $\frac{5}{1512}$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:
Question : The HCF and the LCM of two numbers are 5 and 175, respectively. If the ratio of the two numbers is 5 : 7, the larger of the two numbers is _______.
Question : The LCM of two numbers is five times their HCF. If the product of the two numbers is 20480, then find their HCF and LCM, respectively.
Question : Two numbers are in the ratio 7 : 11. If their HCF is 28, then the sum of the two numbers is:
Question : The sum of the two numbers is 1224 and their HCF is 68. The number of pairs of numbers satisfying the above condition is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile