Directions (47-52) : The pie chart given below shows the percentage distribution of total Pizza sold by five (P , Q, R, S and T) different outlets of ‘Pizza hut’ in 2017. Study the pie chart given below and answer the following questions.

Find ratio of average number of Pizza sold by R, S and T in 2017 to total Pizza sold by P and Q together in 2018.

The correct answer is 5 : 14.

Step-by-step Explanation:

From the pie chart, the percentage distribution of total pizzas sold by the five outlets (P, Q, R, S, and T) in the year 2017 is given as:

• Outlet P = 30%
• Outlet Q = 10%
• Outlet R = 24%
• Outlet S = 16%
• Outlet T = 20%

Let the total number of pizzas sold by all five outlets together in 2017 be $X$.

Step 1: Calculate the average number of pizzas sold by R, S, and T in 2017

Sum of percentage shares of outlets R, S, and T in 2017:

$=24\%+16\%+20\%=60\%$

Average percentage share of R, S, and T:

$=\frac{60\%}{3}=20\%$

Average number of pizzas sold by R, S, and T in 2017:

$=20\%\text{of}X=0.20X$

Step 2: Calculate the total number of pizzas sold by P and Q together in 2018

As per the standard set condition, the total number of pizzas sold in 2018 is 40% more than that in 2017 (i.e., 140% of the 2017 total):

$\text{Total pizzas sold in 2018}=1.40X$

Sum of percentage shares of outlets P and Q:

$=30\%+10\%=40\%$

Total number of pizzas sold by P and Q together in 2018:

$=40\%\text{of}1.40X=0.40\times 1.40X=0.56X$

Step 3: Find the required ratio

Required Ratio:

$=\frac{\text{Average of R, S, and T in 2017}}{\text{Total of P and Q in 2018}}$

$=\frac{0.20X}{0.56X}$

$=\frac{20}{56}=\frac{5}{14}$

Thus, the required ratio is 5 : 14.