The average of a certain number of quantities is 45. If 5 is added to each quantity, what will be the new average?

Correct — B. Let there be n quantities.

Old total = 45 × n = 45n
Adding 5 to each adds 5 × n = 5n
New total = 45n + 5n = 50n
New average = 50n ÷ n = 50 → option (b).

Why the others are wrong

• (a)
  45 — 45 is the old average. Every quantity went up by 5, so the total rose by 5n and the average must rise with it.
• (c)
  40 — 40 subtracts the 5 instead of adding it. Adding a constant to every quantity raises the average by that same constant.
• (d)
  55 — 55 raises the average by 10, but each quantity gained 5. When every value moves up by 5, the average moves up by exactly 5.

Adding the same number to every quantity moves the average up by that same number. The count n cancels, which is why the stem never says how many quantities there are.

Subtracting a constant from every value lowers the average by it. Multiplying every value by k multiplies the average by k.

Adding a number to a single value is different: the average then rises by that number ÷ n.

Key facts

• Average of (each value + c) = old average + c.
• Average of (each value × k) = old average × k.
• Here 45 + 5 = 50, whatever the number of quantities.

Common traps

• Dividing the 5 by the number of quantities, as if a single quantity had been raised.
• Deciding the question cannot be solved because n is not given. The n cancels.

No directly related past PYQ was found.