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P's income is ₹ 140 more than Q's income and R's income is ₹ 80 more than S's. If the ratio of P's and R's incomes is 2:3 and the ratio of Q's and S's incomes is 1:2, then the incomes of P, Q, R and S are, respectively:
We are given that,
P = 140 + Q --(1)
R = 80 + S --(2)
$$\dfrac{P}{R}\ =\ \dfrac{2}{3}$$ --(3)
$$\dfrac{Q}{S}\ =\ \dfrac{1}{2}$$ --(4)
From (4), $$S\ =\ 2Q$$
Substituting the values of (1) and (2) in (3), we get,
$$\dfrac{140\ +\ Q}{80\ +\ S}\ =\ \dfrac{2}{3}$$
$$420\ +\ 3Q\ =\ 160\ +\ 2S$$
Substituting the value of S, we get,
$$420\ +\ 3Q\ =\ 160\ +\ 4Q$$
$$Q\ =\ 420\ -\ 160\ =\ 260$$
$$S\ =\ 2Q\ =\ 2\ \cdot\ 260\ =\ 520$$
$$P\ =\ 140\ +\ Q\ =\ 140\ +\ 260\ =\ 400$$
$$R\ =\ 80\ +\ S\ =\ 520\ +\ 80\ =\ 600$$
The incomes of P, Q, R and S are ₹ 400, ₹ 260, ₹ 600 and ₹ 520, respectively.
Hence, the correct answer is option C.