Study the given table and answer the question that follows.
The table shows the production of five types of cars P, Q, R, S and T by a company from the year 1989 to 1994.
| Type of Car | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | Total |
|---|---|---|---|---|---|---|---|
| P | 8 | 20 | 16 | 17 | 21 | 6 | 88 |
| Q | 16 | 10 | 14 | 12 | 12 | 14 | 78 |
| R | 21 | 17 | 16 | 15 | 13 | 8 | 90 |
| S | 4 | 6 | 10 | 16 | 20 | 31 | 87 |
| T | 25 | 18 | 19 | 30 | 14 | 27 | 133 |
| Total | 74 | 71 | 75 | 90 | 80 | 86 | 476 |
In which year was the total production of cars of types P and Q together equal to the total production of cars of types R and S together?
Correct Answer :
1993
Solution :
To find the year in which the total production of cars of types P and Q together was equal to the total production of cars of types R and S together, we can calculate the combined production for each year and compare them.
Let's calculate the sum of production for P and Q, and the sum of production for R and S, year by year using the data given in the table:
For 1989:
Production of P and Q together = 8 + 16 = 24
Production of R and S together = 21 + 4 = 25
Since 24 ≠ 25, 1989 is not the required year.
For 1990:
Production of P and Q together = 20 + 10 = 30
Production of R and S together = 17 + 6 = 23
Since 30 ≠ 23, 1990 is not the required year.
For 1991:
Production of P and Q together = 16 + 14 = 30
Production of R and S together = 16 + 10 = 26
Since 30 ≠ 26, 1991 is not the required year.
For 1992:
Production of P and Q together = 17 + 12 = 29
Production of R and S together = 15 + 16 = 31
Since 29 ≠ 31, 1992 is not the required year.
For 1993:
Production of P and Q together = 21 + 12 = 33
Production of R and S together = 13 + 20 = 33
Since 33 = 33, the condition is satisfied.
For 1994:
Production of P and Q together = 6 + 14 = 20
Production of R and S together = 8 + 31 = 39
Since 20 ≠ 39, 1994 is not the required year.
Therefore, in the year 1993, the total production of cars of types P and Q together was equal to the total production of cars of types R and S together.
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