If $19a + 19b + 19c = 437$, then what is the mean of $a$, $b$ and $c$?
[amp_mcq option1=”6.33″ option2=”7.66″ option3=”9.33″ option4=”11.55″ correct=”option2″]
This question was previously asked in
UPSC CAPF – 2024
We can factor out the common term 19 from the left side of the equation:
$19(a + b + c) = 437$.
To find the sum $a+b+c$, divide both sides by 19:
$a + b + c = \frac{437}{19}$.
Perform the division:
$437 \div 19$:
$19 \times 2 = 38$. $43 – 38 = 5$. Bring down 7, making it 57.
$19 \times 3 = 57$. $57 – 57 = 0$.
So, $\frac{437}{19} = 23$.
The sum of $a$, $b$, and $c$ is $a+b+c = 23$.
The mean (average) of $a$, $b$, and $c$ is defined as $\frac{a+b+c}{3}$.
Mean = $\frac{23}{3}$.
To express this as a decimal, divide 23 by 3:
$23 \div 3 = 7$ with a remainder of 2. So, $\frac{23}{3} = 7 \frac{2}{3}$.
As a decimal, $\frac{2}{3} \approx 0.666…$.
Mean $\approx 7.666…$.
Looking at the options, 7.66 is the closest approximation, likely rounded to two decimal places.