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?

Correct option is D

Given:

The total pie chart represents 360°.

Given that Soccer (35°) → ₹42,000.

Formula Used:

Money spent on a sport = $$\left(\frac{\text{Degree of sector}}{35} \times 42000 \right)$$​​

Percentage difference = $$\frac{\text{Difference}}{\text{Sum of Cricket, Swimming, Hockey expenses}} \times 100$$​​

Solution:

Since 35° → ₹42,000, the total expenditure is:

Total Expenditure = $$\frac{360}{35} \times 42000$$​ = ₹4,32,000

Expenditure;

Badminton (45°)  = $$\frac{45}{360} \times 4,32,000$$​ = ₹54,000

Tennis (65°) = $$\frac{65}{360} \times 4,32,000$$​ = ₹78,000

Rugby (25°) = $$\frac{25}{360} \times 4,32,000$$​ = ₹30,000

Cricket (100°) = $$\frac{100}{360} \times 4,32,000$$​ = ₹1,20,000

Swimming (60°) = $$\frac{60}{360} \times 4,32,000$$​ = ₹72,000

Hockey (30°) = $$\frac{30}{360} \times 4,32,000$$​ = ₹36,000

Summing up expenditures:

Badminton + Tennis + Rugby = ₹54,000 + ₹78,000 + ₹30,000 = ₹1,62,000

Cricket + Swimming + Hockey = ₹1,20,000 + ₹72,000 + ₹36,000 = ₹2,28,000

Percentage difference: = $$\frac{(2,28,000 - 1,62,000)}{2,28,000} \times 100 = \frac{66,000}{2,28,000} \times 100 = 28.95\%$$ 

Thus, The money spent on Badminton, Tennis, and Rugby is 28.95% less than the money spent on Cricket, Swimming, and Hockey.

Alternate Solution: ​

As only percentage is asked thus we can solve this only using the degrees given ;

Total degrees for Badminton, Tennis, and Rugby = 45 + 65 + 25 = 135 

Total degrees for Cricket, Swimming, and Hockey = 100 + 60 + 30 = 190 

difference = 190 - 135 = 55 

Percentage difference =  $$\frac{55}{190} \times 100 \approx 28.95 \%$$ ​