Rs.43,120 is divided among P, Q and R such that P's share is 4/7 of total share of Q and R together and Q's share is 2/5 of total share of P and R together. What is the share of R?

Rs.15120

ATQ

Ratio of shares:

 P : Q + R = 4 : 7 ⇒ 11 (Total) ........(i)

Q : P + R = 2 : 5  ⇒ 7 (Total) ........(ii)

Multiply (i) by 7 and (ii) by 11 to make the total equal (i.e. 77a)

 P : Q + R = 28 : 49 ⇒ 77 (Total)

Q : P + R = 22 : 55  ⇒ 77 (Total)

Now, We get

P = 28a, Q = 22a and

R = 77a - (P + Q) = 77 - 28 - 22 = 27a

Here,

77a = 43120

1a = 560

R = 27a = 27 × 560 = Rs.15120

Alternate:

Let share of P = P , Share of Q = Q , SHare of R = R

Given:-

P = \(\frac{4}{7}\) (Q+R)

(Q+R) = \(\frac{7}{4}\)P       ---------------(1)

Q = \(\frac{2}{5}\) (P+R)

(P+R) = \(\frac{5}{2}\) Q     -----------------(2)

ATQ ,

P+Q+R = 43120

By using equation 1 ,

P + \(\frac{7}{4}\)P = 43120

\(\frac{11P}{4}\) = 43120

P = 15680

P+Q+R = 43120

By using equation 2 ,

\(\frac{5}{2}\) Q + Q = 43120

\(\frac{7Q}{2}\) = 43120

Q = 12320

&  P+Q+R = 43120 

15680 + 12320 + R = 43120

R = 15120