Question

if m:n=5:9 then find value of (6m+5n):(5m+6n).
1)31/39
2)31/25
3)121/117
4)75/79​

Answer 1

The correct answer is option (4)

(6m+5n):(5m+6n) = 25/79

Given:

m : n = 5 : 9  

To find

The value of (6m+5n):(5m+6n).

Solution:

Given m : n = 5 : 9  

⇒ m/n = 5/9

Here we need find  (6m+5n):(5m+6n).

⇒ $\frac{6m+5n }{5m+6n }$ =  $\frac{n (6\frac{m}{n} +5) }{n(5\frac{m}{n} +6) }$  = $\frac{ (6\frac{m}{n} +5) }{(5\frac{m}{n} +6) }$  

= $\frac{ (6(\frac{5}{9}) +5) }{(5(\frac{5}{9}) +6) }$ = $\frac{ (\frac{10}{3}) +5) }{(\frac{25}{9}) +6) }$ = $\frac{\frac{10+15}{ 3} }{\frac{25+54}{9} }$

= $\frac{15}{3} (\frac{9}{79})$ = $\frac{15}{1} (\frac{3}{79})$ = 25/79

(6m+5n):(5m+6n) = 25/79

The correct answer is option (4)

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