Question 33

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.

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