Question Details

Directions (67-69):The radar graph given below shows the number of buckets (plastic + wooden) sold by five different shops (P , Q, R, S and T) in two different months (May and June). Read the data carefully and answer the questions.

In May, if total wooden buckets sold by R was 200% more than total number wooden buckets sold by S in May and total number of plastic buckets sold by R in May are more than total plastic bucket sold by S in May, then which of the following option cannot be the number of plastic buckets by R in May.

Options

117

120

Both (a) and (c)

Show Answer

Correct Answer :

Option E

Both (a) and (c)

Solution :

Step 1: Extract data from the radar graph for May

Looking at the radar graph for the month of May (represented by the blue line with square markers):
- The value for shop R in May corresponds to the outermost boundary of the radar chart, which is 240.
- The value for shop S in May is explicitly labeled on the graph as 150.

Step 2: Set up the equations for May

Let the number of wooden buckets and plastic buckets sold by shop S in May be $W_{S}$ and $P_{S}$ respectively:
$W_{S} + P_{S} = 150$
This gives:
$P_{S} = 150 - W_{S}$

Similarly, let the number of wooden buckets and plastic buckets sold by shop R in May be $W_{R}$ and $P_{R}$ respectively:
$W_{R} + P_{R} = 240$

Step 3: Use the given relations to form an inequality

We are given that the total wooden buckets sold by R in May was 200% more than that sold by S in May:
$W_{R} = W_{S} + 200 % of W_{S} = 3 W_{S}$

Substituting $W_{R} = 3 W_{S}$ into the total sales for R:
$3 W_{S} + P_{R} = 240 \Rightarrow P_{R} = 240 - 3 W_{S}$

We are also given that the number of plastic buckets sold by R in May is greater than that sold by S in May:
$P_{R} > P_{S}$

Substituting the expressions for $P_{R}$ and $P_{S}$ into this inequality:
$240 - 3 W_{S} > 150 - W_{S}$
$240 - 150 > 3 W_{S} - W_{S}$
$90 > 2 W_{S}$
$W_{S} < 45$

Step 4: Find the range of plastic buckets sold by R in May

Since $W_{S} < 45$ , we can determine the lower bound for $P_{R}$ :
$P_{R} = 240 - 3 W_{S} > 240 - 3 (45)$
$P_{R} > 240 - 135$
$P_{R} > 105$

Thus, the number of plastic buckets sold by R in May must be strictly greater than 105.
Let us evaluate the options:
- 90 is less than 105 (Invalid)
- 117 is greater than 105 (Valid)
- 96 is less than 105 (Invalid)
- 120 is greater than 105 (Valid)

Therefore, the values 90 and 96 cannot be the number of plastic buckets sold by R in May. This corresponds to Both (a) and (c).