Solution
Understanding the set :-
- There are 3 salesmen - Tohri, Hokli and Lahur, who sold 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.
- 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
- 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.
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| 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.
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| T | x | 100 | ||||
| H | x | 100 | ||||
| L | x | 100 |
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
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| T | 2y | 100 | ||||
| H | 2y | 100 | ||||
| L | y | y | 2y | 50 | 50 | 100 |
Clue 2 says,
On both days, Lahur met the same number of households and sold the same number of items.
=> Lahur sold 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 )
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| T | y - 15 | y + 15 | 2y | 100 | ||
| H | 2y | 100 | ||||
| L | y | y | 2y | 50 | 50 | 100 |
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
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| T | y - 15 | y + 15 | 2y | 100 | ||
| H | 2y -1 | 1 | 2y | 100 | 0 | 100 |
| L | y | y | 2y | 50 | 50 | 100 |
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 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 house on day 2
=> he visited households on day 1.
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| T | 10 | 40 | 50 | 40 | 60 | 100 |
| H | 49 | 1 | 50 | 100 | 0 | 100 |
| L | 25 | 25 | 50 | 50 | 50 | 100 |
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
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
=>
=> .
=>
=>
=> .
therefore,
=>
put all the values of y and x in the table.
| Met | Sold | |||||
|---|---|---|---|---|---|---|
| D1 | D2 | Tot | D1 | D2 | Tot | |
| T | 10 | 40 | 50 | 40 | 60 | 100 |
| H | 49 | 1 | 50 | 100 | 0 | 100 |
| L | 25 | 25 | 50 | 50 | 50 | 100 |
The number of households Lahur met on the second day = 25
Hence, between 21 and 29