Let the positive numbers a₁, a₂, a₃, a₄ and a₅ be in a G.P. Let their mean and variance be 31/10 and m/n respectively, where m and n are co-prime. If the mean of their reciprocals is 31/40 and a₃+a₄+a₅=14, then m+n is equal to _ _ _ _ _ _.

Statistics and Probability: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q46

JEE Main 202312 Apr, Morning shiftMathematicsMediumStatistics and Probability258× since 2002

Let the positive numbers

a_{1}, a_{2}, a_{3}, a_{4}

and

a_{5}

be in a G.P. Let their mean and variance be

\frac{31}{10}

and

\frac{m}{n}

respectively, where

m

and

n

are co-prime. If the mean of their reciprocals is

\frac{31}{40}

and

a_{3}+a_{4}+a_{5}=14

, then

m+n

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.