Question

If the sum of LCM and HCF of two numbers is 50 and their LCM is 20 more than their HCF. Then the product of the two numbers will be
a. 525
b. 425
c. 625
d. 325

Answer 1

Hint: In order to find the solution of this question, we will consider the LCM and HCF of the two numbers as x and y respectively. Then, we will try to find the values of LCM and HCF. And we know that the product of two numbers is the product of LCM and HCF of the two numbers. Hence, we will be able to find the answer.

Complete step-by-step solution -
In this question, we have been given that the sum of LCM and HCF of two numbers is 50 and their LCM is 20 more than their HCF. And we have been asked to find the product of the two numbers. Now, to solve this question, we will consider the LCM of two numbers as x and their HCF as y. So, according to the situation given in the question, we can write,
$x + y = 50$ …………….… (i) as the sum of LCM and HCF of two numbers is 50.
And $x = y + 20$ ……...… (ii) as we know that the LCM of the two numbers is 20 more than their HCF.
Now, we will put the value of x from equation (ii) in equation (i). So, we will get,
$y + 20 + y = 50$
Now, we will simplify it to get the value of y. So, we get,
$2y = 50 – 20$
$2y = 30$
We can further write it as,
$y=\dfrac{30}{2}$
$y = 15 $……………..… (iii)
Now, we will put the value of y from equation (iii) to equation (ii). So, we get,
$x = 15 + 20$
We can further write it as,
$x = 35$ ………..……..… (iv)
Hence, we can say that the LCM of the two numbers is 35 and their HCF is 15.
Now, we have been asked to find the product of those two numbers of which we have calculated the LCM and HCF. So, we know that,
Product of two numbers = Product of their LCM and HCF
Therefore, we can say that,
Product of the two numbers = $x\times y$
Now, we will substitute the values of x and y, that is, x = 35 and y = 15. So, we will get,
Product of the two numbers = $35\times 15$
So, we get,
Product of the two numbers = 525
Hence, we can say that the product of two numbers, whose sum of LCM and HCF is 50 and their LCM is 20 more than their HCF, is 525.

Note: While solving this question, the possible mistake one can make is by assuming the two numbers as x and y and then solving the question which may give us the answer but will complicate the answer and will increase the chances of calculation mistakes. So, it is better to assume the LCM as x and the HCF as y and then solve the question. Another possible mistake is that the students may take the condition that the LCM of the two numbers is 20 more than their HCF, and they may write it as $x + 20 = y$, but this is wrong, it must be actually written as, x = y + 20.