Question : Directions: The average income of six friends A, B, C, D, E, and F is INR 6,500. The total income of B, D, E, and F is INR 25,000. If A 's income is INR 4,000 less than C's income, then what is the income of C?
Option 1: INR 10,000
Option 2: INR 9,000
Option 3: INR 7,000
Option 4: INR 8,000
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Correct Answer: INR 9,000
Solution :
(I) The average income of six friends A, B, C, D, E, and F is INR 6,500
The average income of six friends = 6,500 (Average = Total number of observations divided by number of observations)
Total income of six friends = Average × 6
Total income = (A + B + C + D + E + F) × 6 = 6,500 × 6 = 39,000
(II) The total income of B, D, E, and F is INR 25,000.
B + D + E + F = 25,000
(A + B + C + D + E + F) – (B + D + E + F) = 39,000 – 25,000 = 14,000
Thus, (A + C) income = 14,000
(III) If A's income is INR 4,000 less than C's income.
Let C's income be X; A's income be (X – 4000)
X + (X – 4000) = 14,000
2X – 4000 = 14,000
2X = 14,000 + 4000
2X = 18,000; X = 9,000
So, C's income is INR 9,000. Hence, the second option is correct.
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