Multiple choice

P's income is Rs. 140 more than Q's income and R's income is Rs. 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 income of P, Q, R and S are, respectively:

  1. Rs. 260, Rs. 120, Rs. 320 and Rs. 240

  2. Rs. 300, Rs. 160, Rs. 600 and Rs. 520

  3. Rs. 400, Rs. 260, Rs. 600 and Rs. 520

  4. Rs. 320, Rs. 180, Rs. 480 and Rs. 360
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P = Q + 140, R = S + 80. P/R = 2/3, Q/S = 1/2. Substitute: (Q+140)/(S+80) = 2/3. 3Q + 420 = 2S + 160. Since S = 2Q, 3Q + 420 = 4Q + 160. Q = 260. Then S = 520, P = 400, R = 600.

AI explanation

Let Q's income be y, making P's income y + 140. Let S's income be z, making R's income z + 80. The ratio of P's to R's income is 2 : 3, giving 3(y + 140) = 2(z + 80). The ratio of Q's to S's income is 1 : 2, giving z = 2y. Substituting z = 2y into the first equation yields 3y + 420 = 4y + 160, so y = 260. Thus, Q's income is Rs. 260, P's is Rs. 400, S's is Rs. 520, and R's is Rs. 600.

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