Question

The difference between two whole numbers is 66 and one number is four times the other number. It 10 is added to both the numbers, then the ratio can be
A) $15:32$
B) $7:19$
C) $14:39$
D) $16:49$

Answer 1

Hint:
Here, we have to find the ratio between the two whole numbers. For that, we will first assume two whole numbers to any variable and then we will find the difference and equate it with the given difference. Then we will equate the first whole number to four times the other whole number. From there, we will calculate the value of these two whole numbers and then we will add 10 to both and we will find their ratio.

Complete step by step solution:
Let the first whole number be $X$ and let the second whole number be$Y$.
According to the question, their difference is equal to 66.
Therefore,
$\Rightarrow Y-X=66$ …………..$\left(1\right)$
It is given that one of the whole numbers is four times the other whole number.
Therefore,
$\Rightarrow Y=4X$ ………………..$\left(2\right)$
Now, we will put value of $Y$ in equation $\left(1\right)$
$\Rightarrow 4X-X=66$
Subtracting X from 4X, we get
$\Rightarrow 3X=66$
Dividing 66 by 3, we get
$\Rightarrow X={\displaystyle \frac{66}{3}}=22$
Now, we will put the value of $X$in equation $\left(2\right)$
$\Rightarrow Y=4\times 22=88$
Thus, the numbers are 22 and 88.
Now, we will add 10 to both numbers, the numbers become 32 and 98
We will calculate their ratio now.
$\text{required ratio}={\displaystyle \frac{32}{98}}={\displaystyle \frac{16}{49}}$

Therefore, the required ratio between the numbers is 16:49
Hence, the correct option is D.

Note:
Important terms that we need to know are:-
1) All the positive numbers starting from 0 are known as whole numbers and no fractional numbers and decimal numbers are counted in whole numbers.
2) Ratio of two numbers shows the relation between the sizes of the two numbers.
3) If a & b are two numbers and their ratio is a:b . If we multiply both the numbers by the same number then their ratio would be the same.