CAT 2022 Slot 2 · DILR · Question 3

CAT 2022 Slot 2 previous year question on Caselet DI, with the answer and a step-by-step solution.

Caselet DIData InterpretationMultiple choiceMedium

Set 1: TRICCEK Salesmen — this question belongs to a set. Read the full set with all 5 questions →

A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below.

1. Over the two days, all three of them met the same total number of households, and each of them sold a total of 100 items.

2. On both days, Lahur met the same number of households and sold the same number of items.

3. Hokli could not sell any item on the second day because the first household he met on that day complained against him.

4. Tohri met 30 more households on the second day than on the first day.

5. Tohri’s success rate was twice that of Lahur’s on the first day, and it was 75% of Lahur’s on the second day.

How many households did Lahur meet on the second day?

A
between 21 and 29
B
20 or less
C
more than 35
D
between 30 and 35

Pick an option, then check.

Answer & solution

Answer: Option A

Solving the set

Step 1 – Lahur meets h households and sells s items each day (fact 2), so 2s = 100 ⇒ s = 50 per day. All three met the same total, N = 2h.

Step 2 – Hokli met just 1 household on Day 2 (sold 0), so on Day 1 he met N − 1 households and sold 100 items.

Step 3 – Tohri meets t on Day 1 and t + 30 on Day 2: 2t + 30 = 2h ⇒ h = t + 15. Let Tohri sell x items on Day 1 and 100 − x on Day 2.

Step 4 – Fact 5. Day 1: x/t = 2 × 50/(t + 15) ⇒ x = 100t/(t + 15). Day 2: (100 − x)/(t + 30) = 0.75 × 50/(t + 15). Since 100 − x = 1500/(t + 15), this gives 1500 = 37.5(t + 30) ⇒ t = 10, x = 40, h = 25, N = 50.

Salesman	Day 1 households	Day 1 items	Day 1 success rate	Day 2 households	Day 2 items	Day 2 success rate	Total households	Total items
Tohri	10	40	4.00	40	60	1.50	50	100
Hokli	49	100	2.04	1	0	0	50	100
Lahur	25	50	2.00	25	50	2.00	50	100
Total	84	190		66	110		150	300

This question

From Step 4, Lahur met h = 25 households each day, which is between 21 and 29.

Hence, the answer is option 1.

CAT 2022 Slot 2 · DILR · Question 3

More Caselet DI questions