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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 100100 items.
  1. On both days, Lahur met the same number of households and sold the same number of items.
  1. Hokli could not sell any item on the second day because the first household he met on that day complained against him.
  1. Tohri met 3030 more households on the second day than on the first day.
  1. Tohri's success rate was twice that of Lahur's on the first day, and it was 75%75 \% of Lahur's on the second day.

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

Entered answer:

Solution

✅ Correct Answer: 40
Slide 1/8

Understanding the set :-

  1. There are 3 salesmen - Tohri, Hokli and Lahur, who sold a product called TRICCEK among households in various housing complexes.
  1. 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.
  1. 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
  1. 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

In this set we are required to find the number of houses each salesmen met, and the number of products sold by him.

So lets first make a table where we can Clearly write down all the given clues in the set.

MetSold
D1D2TotD1D2Tot
T
H
L

In this table we have in first three columns the number of households met by three salesmen on day 1 (D1) , day 2 (D2) and it's total

Also, the last three columns consist of number of products sold by three salesmen in day 1 , day 2 and it's total

Here T, H, L represents Tohri, Hokli and Lahur respectively.

MetSold
D1D2TotD1D2Tot
Tx100
Hx100
Lx100

Clue 1 says.

Over the two days, all three of them met the same total number of households,

Let the total number of houses they met be "x"

and each of them sold a total of 100 items.

=> total number of products sold by each of them is 100

MetSold
D1D2TotD1D2Tot
T2y100
H2y100
Lyy2y5050100

Clue 2 says,

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

=> Lahur sold 5050 products each in day 1 and day2.

Also, let the number of household met by lahur be "y"

=> total number of households met by him = 2y

=> total number of households met by each salesmen = 2y (according to clue 1 )

MetSold
D1D2TotD1D2Tot
Ty - 15y + 152y100
H2y100
Lyy2y5050100

Using clue 4,

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

Let Tohri met "a" households on day 1

=> he will meet "a + 30 " households on day 2

=> a + a + 30 = 2y

=> 2a + 30 = 2y

=> a = y - 15

Therefore, households met by Tohri on day 1 = y - 15

and, on day 2 = y - 15 + 30 = y + 15

MetSold
D1D2TotD1D2Tot
Ty - 15y + 152y100
H2y -112y1000100
Lyy2y5050100

Using clue 3,

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

=> Hokli sold ′0′'0' products on D2

Therefore, he sold all 100 items on D1 itself.

Also, he got complained in the very first household on the second day

=> he visited only ′1′'1' house on day 2

=> he visited 2y−12y - 1 households on day 1.

MetSold
D1D2TotD1D2Tot
T1040504060100
H491501000100
L2525505050100

Clue 6 says,

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.

let the number of products sold by Tohri on D1 be ′x′'x'

we know, 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

=> x/(y−15)=(50/y)∗2x / (y -15) = (50 / y) *2

=> xy=100(y–15)xy = 100(y–15).

=> 4x(100–x)=150(y+15)4x(100–x) = 150(y+15)

=> 400y–4xy=150(y+15)400y – 4xy = 150(y+15)

=> 400y–4∗100(y–15)=150(y+15)400∗15=150(y+15)400y – 4*100(y–15) = 150(y+15) 400 * 15 = 150 (y+15).

therefore, y=25y = 25

=> x=40x = 40

put all the values of y and x in the table.

MetSold
D1D2TotD1D2Tot
T1040504060100
H491501000100
L2525505050100

Tohri sold 40 products on D1

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