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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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The average monthly income of P and Q is ₹5,050. The average monthly income of Q and R is ₹6,250 and the average monthly income of P and R is ₹5,200. The monthly income of P (in ₹) is:
4,000
4,050
5,000
3,500
4,000
Sum all equations to get 2(P+Q+R)=(5050+6250+5200)×2=33000. Thus P+Q+R=16500. Subtract (Q+R) from the total to find P=16500−12500=4000.
Average income of P+Q = ₹5050, Q+R = ₹6250, P+R = ₹5200.
(P+Q)+(Q+R)+(P+R)=2(P+Q+R)
Sum all equations to get 2(P+Q+R)=(5050+6250+5200)×2=33000. Thus P+Q+R=16500. Subtract (Q+R) from the total to find P=16500−12500=4000.
Forgetting that the given values are averages, not total sums. One must multiply the average by 2 to get the total monthly income for each pair.
Calculate total monthly incomes
Since the average of two people is the sum divided by 2, we multiply each average by 2 to find the total income: P+Q=5050×2=10100, Q+R=6250×2=12500, P+R=5200×2=10400.
P+Q=10100,Q+R=12500,P+R=10400
Sum the equations
Adding all three equations: (P+Q)+(Q+R)+(P+R)=2(P+Q+R)=10100+12500+10400.
2(P+Q+R)=33000
Find sum of all
Divide by 2 to get the combined monthly income of P, Q, and R: P+Q+R=33000/2=16500.
P+Q+R=16500
Solve for P
Subtract the income of Q+R from the total: P=(P+Q+R)−(Q+R)=16500−12500=4000.
P=4000
A is correct because the calculated monthly income of P is ₹4,000.
This type of cyclic sum equation is common in age problems and mixtures; always look for the symmetry 2(A+B+C) to simplify your work quickly.
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