The following table shows the number of pages printed by 3 printers (P, Q and R) for 3 days. What is the ratio of the total number of pages printed by printer P over the course of three days to the total number of pages printed by printer Q during the same three days?

Correct — B. Each printer owns a column, so total down the column, not across the row.

Printer P: 100 + 120 + 180 = 400
Printer Q: 130 + 145 + 85 = 360

The stem names P first, so the ratio is P : Q in that order.
400 : 360 = 40 : 36 = 10 : 9

That is option (b).

Why the others are wrong

• (a)
  11 : 10 — Option (a), 11 : 10, would need P to total 440 against Q's 400. The columns give P 400 and Q 360, so neither printer reaches 440.
• (c)
  10 : 11 — Option (c), 10 : 11, would need Q's three days to reach 440. Q prints 130, 145 and 85, which is 360 — well under P's total, not above it.
• (d)
  9 : 10 — Option (d), 9 : 10, is the right arithmetic in the wrong order. 360 : 400 does reduce to 9 : 10, but that answers Q : P, and the stem asks for P first.

A day-by-printer grid can be read two ways, and the question decides which. Three days of one printer is a column, so P's answer comes from going down the P column.

Ratios then need two things: the totals, and the order the stem names them in. Reversing the order gives a number that is also on the option list.

Reduce fully. 400 : 360 goes to 40 : 36 on dividing by 10, and only the further division by 4 reaches 10 : 9.

Key facts

• Printer P prints 100, 120 and 180 pages, a three-day total of 400.
• Printer Q prints 130, 145 and 85 pages, a three-day total of 360.
• 400 : 360 divides by 40 to give 10 : 9.

Common traps

• Adding across a row, which totals one day for all three printers instead of three days for one.
• Answering Q : P when the stem named P first, since 9 : 10 is sitting in the options.
• Stopping at 40 : 36 and never dividing through by the last common factor of 4.

No directly related past PYQ was found.