true

Take Class 8 Tuition from the Best Tutors

• Affordable fees
• 1-1 or Group class
• Flexible Timings
• Verified Tutors

Search in

# Using reverse methodology in solving tricky math problems

09/03/2019 0 0

Hi,

In this lesson, I will demonstrate how to solve a tricky problem (asked in a non regular manner) using reverse methods.

Problem Statement:

2 Numbers x and y are in ratio 3:4 and there LCM is 48, Find the 2 numbers x and y.

Explanation:

This problem is different from a standard regular problem, which asks to calculate LCM of 2 numbers.
So, we will first start by solving a regular problem and see, how we can derive a formula to solve the reverse problem statement.

Regular problem is, Find LCM of 12 and 16.

We take factors of 12    = 2 x 2 x 3.
Then take factos of 16  = 2 x 2 x 2 x 2.

The LCM would be taking the longest occuring natural number, among all factors.
Here factor 2 occurs longest as 4 times, and factor 3 occurs longest once.

Hence LCM =  2 x 2 x 2 x 2 x 3 = 48.

Now, If we analyze the factors of 12 ( 2 x 2 x 3 ) and 16 ( 2 x 2 x 2 x 2 ), and take ratio of 12/16, then we remove the common factors (2 x 2) and are left with ( 3 / (2 x 2) ) = 3 / 4.

Doesn't this look like the original problem mentioned above, x and y are in ration 3:4 .... ?

So now, the common factors that we removed by taking ration of 12 and 16, lets call it 'k' where k = ( 2 x 2 ).

While taking LCM, we will calculate it as k x (remaining non common factors ) = k x (2 x 2 x 3).

hence, If LCM = 48 (LCM of x and y) then 48 = k x (2 x 2 x 3). Hence, k = 4.

Therefore, x / y = ( 3 x k ) / ( 4 x k). Which gives, x = 12, and y = 16.

This way through using the regular method of calculating LCM, we were able to derive a formula to calculate 2 numbers
whose ratio and LCM is already given.

x = k x (numerator of ratio)

y = k x (denominator of ratio)

0 Dislike

## Other Lessons for You

How Is Plastic Useful In Healthcare Industry?
1. Question: How is plastic useful in healthcare industry? Answer: In healthcare, plastics are used a. For packaging of tablets, b. As threads for stitching wounds, c. Doctor gloves, d. In syringes,...

Understand what LCM and HCF is.
LCM- LCM stands for least common multiple The least common multiple of two numbers is the smallest number that is a multiple of both of them or the number which can be commonly multiplied by both the...
S

### Looking for Class 8 Tuition ?

Learn from Best Tutors on UrbanPro.

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you

X

### Looking for Class 8 Tuition Classes?

The best tutors for Class 8 Tuition Classes are on UrbanPro

• Select the best Tutor
• Book & Attend a Free Demo
• Pay and start Learning

### Take Class 8 Tuition with the Best Tutors

The best Tutors for Class 8 Tuition Classes are on UrbanPro