Sign in
Please select an account to continue using cracku.in
↓ →
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.
Click on the Email ☝️ to Watch the Video Solution
Crack IPMAT 2026 with Cracku
Educational materials for IPMAT and IIMB UG preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.