Question

If the ratio of `H.M.` and `G.M.` between two numbers `a` and `b` is `4:5`, then find the ratio of the two number ?
A. `4:1`
B. `3:2`
C. `3:4`
D. `2:3`

Answer 1

Correct Answer - A
Let the numbers be a and b. Then,
`((2ab)/(a+b))/(sqrt(ab))=(4)/(5)`
`rArr" "(2sqrt(ab))/(a+b)=(4)/(5)`
`rArr" "(a+b)/(2sqrt(ab))=(5)/(4)`
`rArr" "(a+b+2sqrt(ab))/(a+b-2sqrt(ab))=(5+4)/(5-4)" "{:[("Applying componendo"),("and dividendo")]:}`
`rArr" "((sqrt(a)+sqrt(b))/(sqrt(a)-sqrt(b)))^(2)=(9)/(1)`
`rArr(sqrt(a)+sqrt(b))/(sqrt(a)-sqrt(b))=(3)/(1)rArr(sqrt(a))/(sqrt(b))=(3+1)/(3-1)rArr(a)/(b)=(4)/(1)`