CAT 2020 Slot 3 — DILR Question 9
Answer the next 4 questions based on the information given.
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery.
The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day.
It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively.
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Among the following days, the largest fraction of orders booked on which day was lost?
Answer & solution
- A
16th
- B
13th
- C
14th
15th
It is given that 4 order which were booked on 11th day were delivered on 13th day.
⇒ Out of 11 orders delivered on 13th day, 11 – 4 = 7 were booked on 12th day.
Out of total orders booked on 12th day 6 were delivered on 14th day and 1 order was lost at the end of the 14th day.
∴ Total orders booked on 12th day = 7 (delivered on 13th day) + 6 (delivered on 14th day) + 1 (lost at the end of 14th day) = 14.
Similarly,
Total orders booked on 13th day = 21 (delivered on 14th day) + 8 (delivered on 15th day) + 2 (lost at the end of 15th day) = 31.
Total orders booked on 14th day = 249 – 219 = 30.
Out of these 30 orders 23 – 8 = 15 orders were delivered on 15th day.
Also, of the orders booked on 14th day orders lost om 16th day = 12.
∴ Of the orders booked on 14th day orders delivered on 16th day = 30 – 15 – 12 = 3.
Similarly, we can make the following table for orders booked and delivered.
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Fraction of orders booked on 13th day which were lost = 2/31
Fraction of orders booked on 14th day which were lost = 12/30
Fraction of orders booked on 15th day which were lost = 12/28
Fraction of orders booked on 16th day which were lost = 2/25
Largest of these fractions is 12/28 i.e., for 15th day.
Hence, option (d).