The following table gives zone wise survey report of the people of a country who take tea. Study the table and answer the question. The ratio of the total number of people surveyed who take tea more than 3 times a day to the number of people who do not take tea at all is

Correct — D. Two whole rows have to be totalled across all four zones, then reduced.

More than 3 times a day: 1732 + 1842 + 6045 + 2741 = 12,360
Never: 317 + 127 + 223 + 293 = 960
So the ratio is 12,360 : 960

Both totals are divisible by 120: 12,360 = 120 × 103 and 960 = 120 × 8.
Ratio = 103 : 8 → option (d).

Why the others are wrong

• (a)
  5 : 107 — 12,360 is nearly 13 times 960, so the larger number has to lead. 5 : 107 puts the small one first and does not reduce from these totals either.
• (b)
  8 : 103 — 8 : 103 is the right ratio written backwards. The question names the more-than-3-times group first, so 12,360 leads and 960 follows.
• (c)
  101 : 5 — 101 : 5 is not the reduced form of 12,360 : 960. Their HCF is 120, which gives 103 and 8, not 101 and 5.

A two-way table asks you to read in one direction and ignore the other. Here every column is a zone and every row is a tea-taking habit, so a question about habits needs whole rows summed across East, West, North and South.

The arithmetic is only addition. The marks are lost in the reading — taking one zone instead of all four, or picking the wrong habit row.

Reduce at the very end, using the HCF of the two totals rather than cancelling zone by zone.

Key facts

• The "more than 3 times a day" row totals 12,360 across the four zones.
• The "Never" row totals 960 across the four zones.
• 12,360 and 960 share an HCF of 120, so the ratio reduces to 103 : 8.

Common traps

• Using the "Only once a week" row for people who do not take tea at all
• Totalling one zone's column instead of a habit row
• Writing the ratio in the reverse order to the one the question states

No directly related past PYQ was found.