Question

Ifa : b=c:d=e: f= 2:1, then (a + 2c + 3e) : (5b + 10d + 15f) is equal to:​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

$\sf{a : b=c:d=e: f= 2:1}$

TO DETERMINE

$\sf{ (a + 2c + 3e) : (5b + 10d + 15f)}$

EVALUATION

It is given that

$\sf{a : b=c:d=e: f= 2:1}$

$\displaystyle \: \implies \sf{ \: \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{2}{1} \: }$

$\displaystyle \: \implies \sf{ a = 2b \: ,\: c = 2d \: , \: e = 2f\: }$

Hence

$\sf{ (a + 2c + 3e) : (5b + 10d + 15f)}$

$= \displaystyle \: \sf{ \frac{ (a + 2c + 3e)}{(5b + 10d + 15f)} }$

$= \displaystyle \: \sf{ \frac{ (2b + 4d + 6f)}{(5b + 10d + 15f)} }$

$= \displaystyle \: \sf{ \frac{ 2(b + 2d + 3f)}{5(b + 2d + 3f)} }$

$= \displaystyle \: \sf{ \frac{2}{5} }$

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Answer 2

HELLO DEAR,

GIVEN:- a : b = c : d = e : f = 2 : 1

therefore,

• a/b = 2/1 => a = 2b
• c/d = 2/1 => c = 2d
• e/f = 2/1 => e = 2f

NOW,

we have to find, (a + 2c + 3e) : (5b + 10d + 15f)

by using above substitution,

we get,

=> {2b + 2(2d) + 3(2f)} : (5b + 10d + 15f)

=> (2b + 4d + 6f) : (5b + 10d + 15f)

=> 2(b + 2d + 3f) : 5(b + 2d + 3f)

=> 2 : 5

hence,(a + 2c + 3e) : (5b + 10d + 15f) = 2 : 5

I HOPE IT'S HELP YOU DEAR,

THANKS