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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:

Solution

✅ Correct Option: 3

Let the incomes of P, Q, R, and S be ₹ p,q,r,sp, q,r, s respectively.

Thus,

p=q+140→q=p−140p=q+140 \rightarrow q = p -140

r=s+80r = s +80

pr=23→r=3p2\frac{p}{r} = \frac{2}{3} \rightarrow r = \frac{3p}{2}

qs=12→s=2p−280\frac{q}{s} = \frac{1}{2} \rightarrow s = 2p - 280

We know, r=s+80r = s + 80

3p2=2p−280+80\frac{3p}{2} = 2p - 280 + 80

3p=4p−4003p = 4p - 400

p=400p =400

There is only one option for the income of P as ₹400.

Hence, the correct option is Option 3.

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