A sum of money is equally divided among a number of children. Had there been…
2024
A sum of money is equally divided among a number of children. Had there been 10 children less, each would have received ₹5 more, and had there been 10 children more each would have received ₹3 less. What is the sum of money that is distributed?
- A.
300
- B.
600
- C.
750
- D.
900
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Let n = number of children and x = each child's original share. The total sum T = n·x is constant in all three cases.
Condition 1 (10 fewer children, ₹5 more each): (n − 10)(x + 5) = nx, which expands to 5n − 10x − 50 = 0.
Condition 2 (10 more children, ₹3 less each): (n + 10)(x − 3) = nx, which expands to −3n + 10x − 30 = 0.
Short approach: just ADD the two expanded equations. The 10x and −10x cancel, giving (5n − 50) + (−3n − 30) = 0 → 2n − 80 = 0 → n = 40 directly — no substitution needed.
Now use any one condition: 5(40) − 10x − 50 = 0 → 200 − 10x − 50 = 0 → x = 15.
Total sum T = n·x = 40 × 15 = ₹600.
Quick check: 30 children → 600/30 = ₹20 (₹5 more ✓); 50 children → 600/50 = ₹12 (₹3 less ✓). So the answer is ₹600.