If (ay − bx)/c = (cx − az)/b = (bz − cy)/a, then which of the following is/are correct ? 1. x/a = y/b. 2. (x + y + z)/(a + b + c) = z/c. Select the correct answer using the code given below:

CDS 2021 PYQ with Answer — If (ay − bx)/c = (cx − az)/b = (bz − cy)/a, then which of the followi…

2021 · Q29

If (ay − bx)/c = (cx − az)/b = (bz − cy)/a, then which of the following is/are correct ?

1x/a = y/b.
2(x + y + z)/(a + b + c) = z/c.

Select the correct answer using the code given below:

Elementary MathematicsRatio and Proportion

A1 only
B2 only
CBoth 1 and 2
DNeither 1 nor 2

Explanation

If (ay−bx)/c = (cx−az)/b = (bz−cy)/a, the standard componendo argument shows x/a = y/b = z/c (each common ratio is consistent). Then (x+y+z)/(a+b+c) equals the same common value, hence equals z/c. Both statements 1 and 2 are correct, option (c).