The given pie chart shows the amount of money (₹) spent (in degrees) on various sports by a sports academy in a particular year. Study the pie chart and answer the question that follows. If ₹42,000 were spent on Soccer, then the money spent on Badminton, Tennis and Rugby taken together is what percentage (rounded off to 2 decimal places) more/less than the money spent on Cricket, Swimming and Hockey taken together?
- (a)Less, 28.95%
- (b)Less, 34.87%
- (c)More, 34.87%
- (d)More, 28.95%
Answer
Why
Correct — A. Read the sectors off the pie: Cricket 100°, Swimming 60°, Badminton 45°, Tennis 65°, Soccer 35°, Rugby 25°, Hockey 30° — they sum to 360°.
Badminton + Tennis + Rugby = 45 + 65 + 25 = 135°
Cricket + Swimming + Hockey = 100 + 60 + 30 = 190°
Difference = 190 − 135 = 55°
The comparison is made against the Cricket group, so 190° is the base:
55⁄190 × 100 = 28.947…% → 28.95%
135° is below 190°, so the first group is less, not more — option (a).
Why the others are wrong
- (b)Less, 34.87% — The direction is right and the figure is not: 34.87% comes from neither base. The 55° gap is 28.95% of 190° and 40.74% of 135°.
- (c)More, 34.87% — Wrong on both counts. The Badminton group is the smaller of the two at 135° against 190°, and 34.87% is not what 55⁄190 or 55⁄135 returns.
- (d)More, 28.95% — The arithmetic is right and the direction is reversed. 28.95% is how far below the Cricket group the Badminton group sits, so the reading is less, not more.
Concept
A pie chart labelled in degrees is a pie chart with the percentages hidden one step back: the whole circle is 360°, so any sector's share of the total is its angle over 360.
Because both groups are read off the same chart, the money scale cancels. A percentage-more/less comparison between two groups of sectors can be settled from the angles alone.
The one decision left is the base. A is x% less than B always divides by B, the quantity being compared against — here the Cricket, Swimming and Hockey group.
The ₹42,000 spent on Soccer never enters the ratio. It fixes the scale at 1° = ₹1,200, which you would need only if the question asked for a rupee figure.
Key facts
- In a pie chart the full circle is 360°, so a sector's share of the total is its angle divided by 360.
- The seven sectors here are Cricket 100°, Tennis 65°, Swimming 60°, Badminton 45°, Soccer 35°, Hockey 30° and Rugby 25°.
- A is x% less than B is computed as (B − A) ÷ B × 100, dividing by B.
- 55⁄190 × 100 = 28.947%, which rounds to 28.95% at two decimal places.
Study next
Common traps
- Dividing by the smaller group at 135° instead of the base named in the question, which returns 40.74%.
- Answering more because the Badminton group is named first in the sentence.
- Converting every sector into rupees when the ₹42,000 cancels out of the ratio.
SSC also runs this in reverse: 24 Sep 2024, 16:00, Quant Q.9 gives the total expenditure and asks for the central angle of one named sector. Straight percentage-of-total reading off a pie appears at 18 Sep 2024, 09:00, Quant Q.3, where 1,200 fruits are sold in a day.
Related PYQs
No directly related past PYQ was found.