Divide rupees 760 among ABC such that a gets 5-6 of world biggest and the ratio between the shares of B and C is 324 explain in simple language
Answers
☺️Hyy Dude ☺️
The division would be A=200; B=240 and C=320
Step-by-step explanation:
Let a, b and c be the amounts that are to be divided between A, B and C, respectively.
Thus: a + b + c = 760 ........(Eqn 1)
We are given that
A gets 5/6 of what B gets
=> a = (5/6)*b
=> 6a = 5b...............(Eqn 2)
Also, ratio between shares of B and C is 3:4
=> b/c = 3/4
=> 4b = 3c............(Eqn 3)
We now need to express "a" in terms of "c". Multiply (Eqn 2) by 4 and (Eqn 3) by 5. This is done to get the same coefficient for "b" in both the equations.
24a = 20b and
20b = 15c
From the above two equations, we get:
24a = 15c
=> a = (15/24)*c
=> a = (5/8)*c .........(Eqn 4)
From (Eqn 3), we get:
b = (3/4)*c ..........(Eqn 5)
Using Eqn 4 and Eqn 5, in Eqn 1, we get:
(5/8)*c + (3/4)*c + c = 760
5c/8 + 3c/4 + c = 760
Taking 8 as the common denominator, we get:
(5c + 6c + 8c)/8 = 760
19c = 8*760
c = (8*760)/19
c = 320
Using (Eqn 4) and (Eqn 5), we get:
a = (5/8)*320 = 200
b = (3/4)*320 = 240
Verify:
a = 200; b = 240 ; c 320
200 = (5/6)*240 = 200
Ratio of b and c is 240:320 = 3:4
Sum of a, b and c = 200+240+320 = 760
Hope it's helps you
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