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.

Day | Cumulative orders booked | Orders delivered on day | Cumulative orders lost |

13th | 219 | 11 | 91 |

14th | 249 | 27 | 92 |

15th | 277 | 23 | 94 |

16th | 302 | 11 | 106 |

17th | 327 | 21 | 118 |

18th | 332 | 13 | 120 |

19th | 337 | 14 | 129 |

**Question 1: **

Among the following days, the largest fraction of orders booked on which day was lost?

- 14th
- 13th
- 15th
- 16th

**Show Answer**

**3**

**Question 2: **

On which of the following days was the number of orders booked the highest?

- 13th
- 15th
- 12th
- 14th

**Show Answer**

**1**

**Question 3: **

The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the next day to the number of orders booked on that day which are delivered on the second day after booking. On which of the following days, was the delivery ratio the highest?

- 13th
- 16th
- 14th
- 15th

**Show Answer**

**3**

**Question 4: **

The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered the next day be x and the number of orders delivered the day after be y. Then the average time to deliver order is (x+2y)/(x+y). On which of the following days was the average time taken to deliver orders booked the least?

- 14th
- 16th
- 15th
- 13th

**Show Answer**

**1**

**Question 1:**

\(14^{\text {th }}\) day \(\Rightarrow 30\) Booked \(\Rightarrow 12\) loss \(\Rightarrow \frac{12}{30}\)

\(13^{ th } day \Rightarrow 31\) Booked \(\Rightarrow 2\) loss \(=\frac{2}{31}\)

\(16^{\text {th }}\) day \(\Rightarrow 25\) Booked \(\Rightarrow 2\) loss \(\Rightarrow \frac{2}{25}\)

\(15^{\text {th }}\) day \(\Rightarrow 28\) Booked \(\Rightarrow 12\) loss \(\Rightarrow \frac{12}{28}\)

The highest value is \(\frac{12}{28},\) on the \(15^{\text {th }}\) day.

Option: 3**Question 2:**

Highest order Booked on \(13^{\text {th }}\) day.

Option: 1**Question 3:**

Delivery ratio \(=\frac{\text { Next day }}{\text { day after }}\)

a. \(13^{\text {th }}\) day \(\Rightarrow \frac{21}{8}\)

b. \(15^{\text {th }}\) day \(\Rightarrow \frac{8}{8}\)

c. \(14^{\text {th }}\) day \(\Rightarrow \frac{15}{3}\)

d. \(16^{\text {th }}\) day \(\Rightarrow \frac{13}{10}\)

The highest ratio is \(\frac{15}{3},\) on \(14^{\text {th }}\) day

Option: 3**Question 4:**

The least is on the \(14^{\text {th }}\) day.

Option: 1### CAT 2020 LRDI sets with Solutions

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