Question

Which of the following options will give the same estimated difference as for $55$ from $82$ when rounded to the nearest tens?

• A. $57$ and $31$
• B. $34$ and $43$
• C. None of the above
• D. Both a and b

Answer 1

The correct option is C None of the above

Let us solve each option by rounding to the nearest tens to get the same estimated difference as for $55$ from $82$ .

The rounding digits in $82$ and $55$ are $8$ and $5$ respectively.
The digits to the right of the rounding digits is $2$ in the case of $82$ and $5$ in the case of $55.$

$82$ lies between $80$ and $90.$



Also, $82$ lies on the left side of the hill.
$82$ closer to $80$.
Since $82$ is closer to $80$, it will be rounded off to $80.$

Now, let’s repeat this process for $55.$



Since $55$ lies at the center, it is closer to $60.$
Hence, the closest ten is $60.$

The difference of the numbers after rounding off $=80-60=20$

Let us solve each option by rounding to the nearest tens to get the estimated difference of $20.$

For option a) $34$ and $43$
The rounding digits in $34$ and $43$ are $3$ and $4$ respectively.
The digits to the right of the rounding digits are $4$ in the case of $34$ and $3$ in the case of $43.$

$34$ lies between $30$ and $40.$


Also, $34$ lies on the left side of the hill.
$34$ closer to $30$.
Since $34$ is closer to $30$, it will be rounded off to $30$.

Now, let’s repeat this process for $43$.



Since $43$ lies on the left side of $45$, it is closer to $40$.
Hence, the closest ten is $40.$

The difference of the numbers after rounding off $=40-30=10$

Hence, the estimated difference of $34$ and $43$ when rounded to the nearest tens is $10.$
Option A is incorrect.

For option b) $57$ and $31$

$57$ lies between $50$ and $60.$

Also, $57$ lies on the right side of the hill.
$57$ closer to $60.$
Since $57$ is closer to $60$, it will be rounded off to $60.$

$31$ lies between $30$ and $40.$


Also, $31$ lies on the left side of the hill.
$31$ closer to $30.$
Since $31$ is closer to $30,$ it will be rounded off to $30.$

The difference of the numbers after rounding off $=60-30=30$

Hence, the estimated difference of $57$ and $31$ when rounded to the nearest tens is $30.$
Option B is incorrect.

Hence, we can see the estimated difference for none of the options is $20.$
Option D is correct.