Divide Rs 2,100 among P, Q and R, so that P shall receive 3/7 as much as Q and R together, and Q  2/3 of what P and R together receive. Find the share of Q.

Let P receives Rs x P = 3/7(Q+R ) ⇒ x = 3/7(Q+R ) ⇒ 7/3 x = Q + R & we know that P+Q+R = 2100 So  x + 7/3 x = 2,100⇒ 10/3 x = 2,100 ∴x = Rs 630 Now,  7/3 x = Q + R ⇒ 7/3  ×630= Rs 1,470 ∴  Q + R = Rs 1,470………………. .(i) Q = 2/3  (P+R )⇒ Q = 2/3  (630+R) ⇒ 3 Q = 1,260 + 2 R ∴  3Q – 2R = Rs 1,260…………………… (ii) Solving (i) and (ii) , we get Q’ share = Rs 840 ALTERNATE SHORTCUT METHOD: Q = 2/3  (P+R )     OR P+R  = 3/2Q  ---(i)  & we know that P+Q+R = 2100   ---(ii) So putting equation (i) in (ii), Q+ 3/2Q  = 2100 Or  5/2Q = 2100   or Q  = 2100/5×2=840