1,875 is divided among A, B and C in such a way that A's share is half of the combined share of B and C, and B's share is one-fourth of the combined share of A and C. By what amount is C's share more than that of A?
Answers
Answer:
C's share is more than the share of A by Rs 250.
Step-by-step explanation:
Given,
Total amount = Rs 1,875.
Total amount is completely divided among A, B and C.
Let,
Share of A be Rs a.
Share of B be Rs b.
Share of C be Rs c.
So,
= > amount of share of A + amount of share of B + amount of share of C = Rs 1875
= > Rs a + Rs b + Rs c = Rs 1875
= > a + b + c = 1875 ...( 1 )
Given : A's share is half of the combined share of B and C
= > Rs a = Half of share of B and C
= > Rs a = ( Share of B and C ) / 2
= > Rs a = ( Rs b + Rs c ) / 2
= > a = ( b + c ) / 2 ....( 2 )
Thus, 2a = b + c → 2a - b - c = 0
Adding ( 2 ) to ( 1 ) :
= > a + b + c + ( 2a - b - c ) = 1875 + 0
= > a + b + c + 2a - b - c = 1875
= > 3a = 1875
= > a = 625
Also,
= > B's share = 1 / 4 of ( Share of A and share of C )
= > Rs b = 1 / 4 of ( Rs a + Rs c )
= > b = 1 / 4 x ( a + c )
= > 4b = a + c
= > 4b - a - c = 0 ... ( 3 )
Adding ( 1 ) and ( 3 ) :
= > 4b - a - c + ( a + b + c ) = 1875
= > 4b - a - c + a + b + c = 1875
= > 5b = 1875
= > b = 375
Thus,
= > 625 + 375 + c = 1875
= > 1000 + c = 1875
= > c = 1875 - 1000
= > c = 875
Thus,
Share of A = Rs 625
Share of B = Rs 375
Share of C = Rs 875
Hence,
C's share is more than the share of A by Rs ( 875 - 625 ) i.e. Rs 250
B+C : A = 2:1
A+C : B = 4:1
B+C = 2A.........(i)
A+C = 4B.........(ii)
Adding both (i) & (ii) we get,
3A=5B
Or
We can say, A:B=5:3.
We know that,
B+C:A = 2:1
Then, Share of A = 1875*1/3 = Rs 625
We also know that A:B=5:3 (we have already found the value of 5 which is A's share - 625)
If
5= 625
Then,
1= 625/5
And
3 = (625/5) *3 =Rs 375 (share of B)
C's share= 1875-625-375 =Rs. 875.
Required answers-> C's share - A's share
875-625 = Rs 250.
