The average of 35 consecutive natural numbers is N. If the first…
The average of 35 consecutive natural numbers is N. If the first 10 numbers are removed, and the next 10 numbers are included, then this average becomes M. If M² − N² = 600, then what will be the average of 3M and 5N?
35 क्रमागत प्राकृतिक संख्याओं का औसत N है। यदि पहली 10 संख्याएँ हटा दी जाएँ तथा अगली 10 संख्याएँ जोड़ दी जाएँ, तो नया औसत M हो जाता है। यदि M² − N² = 600, तो 3M और 5N का औसत क्या होगा?
Detailed Solution & Logic
115
Solution
$M-N=10$
और
$M^2-N^2=600$
इसलिए,
$(M-N)(M+N)=600$
$10(M+N)=600$
$M+N=60$
अब,
$M=35,\ N=25$
3M और 5N का औसत:
$\frac{3M+5N}{2}$
$=\frac{105+125}{2}=115$
Answer: 115
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