TRICCEK Salesmen Performance

CAT 2022 Slot 2 · DILR · Hard · Data Interpretation

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Passage / data set

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.

Question 1 of 5

What was the total number of households met by Tohri, Hokli and Lahur on the first day?

Answer

84

Explanation

Let total households met over 2 days by each salesman be HH. Total items sold by each salesman over 2 days = 100.

For Lahur: On both days, Lahur met the same number of households and sold the same number of items. So on Day 1 and Day 2, Lahur met H2\frac{H}{2} households each day and sold 50 items each day. Lahur's success rate on Day 1 = 50H/2=100H\frac{50}{H/2} = \frac{100}{H}. Lahur's success rate on Day 2 = 100H\frac{100}{H}.

For Tohri: Total households met = HH. Let Day 1 households = h1h_1 and Day 2 households = h2h_2. Given h2=h1+30h_2 = h_1 + 30, so h1+h2=2h1+30=H  ⟹  h1=H−302h_1 + h_2 = 2h_1 + 30 = H \implies h_1 = \frac{H-30}{2} and h2=H+302h_2 = \frac{H+30}{2}. Tohri's success rate on Day 1 is twice Lahur's = 2×100H=200H2 \times \frac{100}{H} = \frac{200}{H}. Items sold by Tohri on Day 1 = Success rate×Households=200H×H−302=100−3000H\text{Success rate} \times \text{Households} = \frac{200}{H} \times \frac{H-30}{2} = 100 - \frac{3000}{H}.

Tohri's success rate on Day 2 is 75% of Lahur's = 0.75×100H=75H0.75 \times \frac{100}{H} = \frac{75}{H}. Items sold by Tohri on Day 2 = 75H×H+302=37.5+1125H\frac{75}{H} \times \frac{H+30}{2} = 37.5 + \frac{1125}{H}.

Total items sold by Tohri = (100−3000H)+(37.5+1125H)=100(100 - \frac{3000}{H}) + (37.5 + \frac{1125}{H}) = 100. 37.5=1875H  ⟹  H=187537.5=5037.5 = \frac{1875}{H} \implies H = \frac{1875}{37.5} = 50.

Now we have H=50H = 50 total households per salesman over 2 days:

  • Lahur met 25 households on Day 1 and 25 on Day 2.
  • Tohri met h1=10h_1 = 10 households on Day 1 and h2=40h_2 = 40 on Day 2.
  • Hokli met 1 household on Day 2 (since the first household complained). Thus Hokli met 50−1=4950 - 1 = 49 households on Day 1.

Total households met by Tohri, Hokli, and Lahur on the first day = 10+49+25=8410 + 49 + 25 = 84.

Question 2 of 5

How many TRICCEK items were sold by Tohri on the first day?

Answer

40

Explanation

Using H=50H = 50 and h1=10h_1 = 10 for Tohri on Day 1: Success rate of Lahur on Day 1 = 50/25=250 / 25 = 2. Tohri's success rate on Day 1 = 2×2=42 \times 2 = 4. Items sold by Tohri on Day 1 = 4×10=404 \times 10 = 40.

Question 3 of 5

How many households did Lahur meet on the second day?

  1. A.

    20 or less

  2. B.

    between 21 and 29

  3. C.

    between 30 and 35

  4. D.

    more than 35

Answer

B

Explanation

Lahur met 25 households on the second day. This lies between 21 and 29.

Question 4 of 5

How many households did Tohri meet on the first day?

  1. A.

    more than 40

  2. B.

    10 or less

  3. C.

    between 11 and 20

  4. D.

    between 21 and 40

Answer

B

Explanation

Tohri met 10 households on the first day, which falls under '10 or less'.

Question 5 of 5

Which of the following statements is FALSE?

  1. A.

    Among the three, Tohri had the highest success rate on the first day.

  2. B.

    Tohri had a higher success rate on the first day compared to the second day.

  3. C.

    Among the three, Lahur had the lowest success rate on the first day.

  4. D.

    Among the three, Tohri had the highest success rate on the second day.

Answer

D

Explanation

Success rates on Day 1:

  • Tohri: 4
  • Lahur: 2
  • Hokli: 100/49≈2.04100 / 49 \approx 2.04 So on Day 1, Tohri (4) > Hokli (2.04) > Lahur (2).

Success rates on Day 2:

  • Tohri: 60/40=1.560 / 40 = 1.5
  • Lahur: 50/25=250 / 25 = 2
  • Hokli: 0 On Day 2, Lahur (2) > Tohri (1.5) > Hokli (0). Therefore, Lahur had the highest success rate on the second day, making option D FALSE.

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