Question
The LCM and HCF of two numbers is 192 and 16 respectively.
If the sum of the number is 112, then find the difference between the numbers.Solution
We know that, LCM X HCF = product of the numbers
Let the numbers are 'a' and 'b'.
So, a X b = 192 X 16
So, ab = 3072........(I)
Given, a + b = 112
From equation (I) ,
Or, 'a' = (3072/b)
So, (3072/b) + b = 112
So, 3072 + b 2 = 112b
Or, b 2 - 112b + 3072 = 0
Or, b 2 - 64b - 48b + 3072 = 0
So, 'b' = 48 or 64
When, 'b' = 48
So, 'a' = (3072/48) = 64
When, 'b' = 64
So, 'a' = (3072/64) = 48
Therefore, required difference = 64 - 48 = 16
Ajay, Bablu and Chirag can complete a certain work in 21, 28 and 15 days respectively. Ajay and Chirag started the work while Bablu joined them after ...
Manoj can complete a job in 10 days which Rakesh can do in 15 days. Rakesh can finish a task in 20 days which Suresh can complete in 25 days. In how man...
‘A’ alone can do some work in 20 days. ‘B’ and ‘C’ together can do the same work in 15 days. If ‘B’ is half as efficient as ‘A’, the...
Rohit is five times as efficient as Sohan and twice as efficient as Mohan. If Sohan takes 15 days to finish some work, then find the time taken by Rohit...
Ashish and Anil can do a piece of work in 10 days and 15 days respectively. Ashish completed 40% of the work. Find the time taken by Anil to complete th...
P and Q can individually complete a piece of work in 30 days and 45 days respectively. If R alone takes 1.5 times the time taken by P and Q together to ...
A contractor planned to complete a project in 5 days by employing ‘a’ workers. But every day exactly 15 workers were absent. As a result, the work g...
‘D’ can type a document in 45 days, but ‘D’ and ‘E’ together can do it in 27 days. If ‘E’ worked for 15 days alone and then left, in how...
Jack is twice efficient as Jill and Jill can do a piece of work in 30 days. Jill started the work and after a few days Jack joined him. They completed t...
Ram can do a piece of work in 12 days and Shyam can do the same work in 16 days. They both started work together, Ram left 2 days before the completion ...
