$a, b, c$ are three positive integers and $2 s = a + b + c$ . If $(s - a) : (s - b) : (s - c) = 1 : 7 : 4$ , then the ratio $a : b : c$ is equal to:

8 : 10 : 6

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11 : 5 : 8

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9 : 4 : 12

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7 : 8 : 9

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Solution

The correct option is B $11 : 5 : 8$
We have,
$(s - a) : (s - b) : (s - c) = 1 : 7 : 4$

So,
$s - a = 1 \Rightarrow a = s - 1$
$s - b = 7 \Rightarrow b = s - 7$
$s - c = 4 \Rightarrow c = s - 4$

Since,
$2 s = a + b + c$
$2 s = s - 1 + s - 7 + s - 4$
$2 s = 3 s - 12$
$s = 12$

Therefore,
$a = 11, b = 5, c = 8$

Hence, the ratio is $a : b : c = 11 : 5 : 8$ .

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a,b,c are three positive integers and 2s=a+b+c. If (s−a):(s−b):(s−c)=1:7:4, then the ratio a:b:c is equal to:

The correct option is B 11:5:8We have,(s−a):(s−b):(s−c)=1:7:4So,s−a=1⇒a=s−1s−b=7⇒b=s−7s−c=4⇒c=s−4Since,2s=a+b+c2s=s−1+s−7+s−42s=3s−12s=12Therefore,a=11,b=5,c=8Hence, the ratio is a:b:c=11:5:8.

$a, b, c$ are three positive integers and $2 s = a + b + c$ . If $(s - a) : (s - b) : (s - c) = 1 : 7 : 4$ , then the ratio $a : b : c$ is equal to: