Question

The number 351 is divided in the ratio 2:7. Find the product of the two numbers.
A. 20294
B. 21294
C. 25295
D. 31294

Answer 1

Hint: We will first let the common factor of the given ratio as $k$. Then, the two numbers will be $2k$ and $7k$. Form an equation such that the sum of these two numbers is 351. Solve the equation to find the value of $k$. Then, find the two numbers and hence, calculate their product.

Complete step-by-step answer:
We are given that the number 351 is divided in the ratio 2:7.
Let the common factor of the ratio be $k$
Then the two numbers in which the 351 is divided are $2k$ and $7k$.
Also, the sum of these two numbers will be equal to 351
$
  2k + 7k = 351 \\
   \Rightarrow 9k = 351 \\
$
Divide both sides by 9
$k = 39$
Substitute the value of $k$ to find the value of two numbers.
$2\left( {39} \right) = 78$ and $7\left( {39} \right) = 273$
We have to find the product of these two numbers.
$78 \times 273 = 21,294$
Hence, option B is correct.

Note: We can write the product of two numbers as $2k\left( {7k} \right) = 14{k^2}$ and directly substitute the value of $k$ in the expression to find the value of product of two numbers instead of finding the two numbers and taking their product.