Question : Three numbers are such that their sum is 50, the product is 3750 and the sum of their reciprocals is $\frac{31}{150}$. Find the sum of the squares of the three numbers.
Option 1: $2500$
Option 2: $1250$
Option 3: $950$
Option 4: $122$
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $950$
Solution : Let the numbers be $a, b$ and $c$. Given: $(a + b + c) = 50$, $abc = 3750$ and $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{31}{150}$ Now, $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{(bc + ac + ab)}{abc}$ ⇒ $\text{(bc+ac +ab)} = \frac{31}{150}\times 3750 = 775$ Also, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)$ ⇒ $(50)^{2} = (a^{2} + b^{2} + c^{2}) + 2(775)$ ⇒ $(a^{2} + b^{2} + c^{2}) = 2500 – 1550$ ⇒ $(a^{2} + b^{2} + c^{2}) = 950$ Hence, the correct answer is $950$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : If the sum of squares of two real numbers is 12 and the product of the numbers is 4, find the difference between the numbers.
Question : The sum of the two numbers is 75, and their difference is 25. The product of the two numbers is:
Question : The ratio of three numbers is 3 : 6 : 8. If their product is 9216, then what is the sum of the three numbers?
Question : If the sum of three consecutive composite numbers is 36, then what is the product of the three numbers?
Question : The ratio of three positive numbers is 2 : 3 : 5 and the sum of their squares is 608. The three numbers are:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile