The H.M. between two numbers is 16/5, their A.M. is A and G.M. is G. If 2A + G2 = 26 then the numbers are

The H.M. between two numbers is 16/5, their A.M. is A and G.M. is G. If $2 A + G^{2} = 26$ then the numbers are

A
6, 8
B
4, 8
C
2, 8
D
1, 8

Solution:

$\begin{array}{l} \frac{2 a b}{a + b} = \frac{16}{5}, a + b + a b = 26 \\ \Rightarrow a + b = \frac{5}{8} a b, a + b + a b = 26 \end{array}$

$∴ \frac{13}{8} a b = 26 \Rightarrow a b = 16$ and $a + b = 10$

Thus, numbers are 2 and 8.

Related content

Download JEE Advanced 2023 Answer Key with Detailed Video Solutions

NCERT Books for Class 12- Download Free PDF (2023-2024)

NCERT Books for Class 6 to 12 – Download Free PDF Updated for 2023-24

Learning Beyond Boundaries: Rohit Sharma’s Vision for Accessible Education

Rohit Sharma: The Cricketer, The Icon – A Biography

ORS Full Form – Oral Rehydration Solution

SDO Full Form – Sub Divisional Officer

ESI Full Form – Employee State Insurance

NEET 2023 Result Date: Check Result, Download NEET UG Result PDF

ESIC Full Form – Employees’ State Insurance Corporation