Rs 2250 is Divided Among Three Friends Amar, Bijoy and Chandra in Such a Way That 1/6th of Amar's Share, 1/4th of Bijoy's Share and 2/5th of Chandra's Share Are Equal. Find Amar's Share

By K Balaji|Updated : November 9th, 2022

(a) Rs 720

(b) Rs 1080

(c) Rs 450

(d) Rs 1240

Amar’s share is Rs 1080.

From the question, we can write as

A/6 = B/4 = 2C/5

Let us multiply all three fractions by LCM(6, 4, 5), we get

10A = 15B = 24C

A + 2A/3 + 5A/12 = 2250

By solving, Amar's share = Rs.1080

Alternative Approach:

Amar's portion needs to be divided by 6. This logic rules out Option D.

A, B, and C together equal 2250. Bijoy's portion should be 480 and Chandra's share must be 300 if Amar's share is 720 (according to option a). (This gives us 720 + 480 + 300 = 1500)

However, the necessary sum is 2250, which is 50% greater than 1500. As all relationships are linear, if we raise all values by 50%, 1500 will become 2250. Amar's share should be 1080 as a result.

LCM 

Finding the smallest common multiple between two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more numbers is said to be a common multiple.

Properties of LCM -

PropertiesDescription
Associative propertyLCM(a, b) = LCM(b, a)
Distributive propertyLCM(da, db, dc) = dLCM(a, b, c)
Commutative propertyLCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c))

How LCM can be calculated?

The smallest common multiple for any two or more given numbers is the least common multiple, as we have already established.

A multiple is the result of multiplying two numbers together. In the same way that 4 is a multiple of 2, we get 4 when we multiply 2 by 2. Similar to the math table, you can observe a number's multiples when you multiply it by the numbers, but not by zero.

Summary:-

Rs 2250 is Divided Among Three Friends Amar, Bijoy and Chandra in Such a Way That 1/6th of Amar's Share, 1/4th of Bijoy's Share and 2/5th of Chandra's Share Are Equal. Find Amar's Share (a) Rs 720 (b) Rs 1080 (c) Rs 450 (d) Rs 1240

Rs 2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 1/6th of Amar's share, 1/4th of Bijoy's share and 2/5th of Chandra's share are equal. Amar’s share is Rs 1080

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