a) KaTeX parse error: KaTeX doesn't work in quirks mode.

b) KaTeX parse error: KaTeX doesn't work in quirks mode.

c) KaTeX parse error: KaTeX doesn't work in quirks mode.

d) KaTeX parse error: KaTeX doesn't work in quirks mode.

correct answer is: d) KaTeX parse error: KaTeX doesn't work in quirks mode.

Explanation

According to the question,
The ratio of KaTeX parse error: KaTeX doesn't work in quirks mode. and KaTeX parse error: KaTeX doesn't work in quirks mode. is KaTeX parse error: KaTeX doesn't work in quirks mode.
Let,
KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
So,
KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
So,
KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode. or KaTeX parse error: KaTeX doesn't work in quirks mode.

Now, KaTeX parse error: KaTeX doesn't work in quirks mode. is decreased KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode. is increased KaTeX parse error: KaTeX doesn't work in quirks mode.
So that, the new ratio of the three angles KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
KaTeX parse error: KaTeX doesn't work in quirks mode.
Ans: The new ratio of the three angles KaTeX parse error: KaTeX doesn't work in quirks mode.

An alternative way to phrase this particular math query is possible:

1. In triangle ABC, the sum of the three angles is 180°. The ratio of ∠BAC, ∠ABC, and ∠ACB is 3 : 5 : 10. If the measure of ∠BAC is reduced by 10° and the measure of ∠ABC is increased by 10°, determine the new ratio of the three angles.
2. The total of the three angles in triangle ABC is 180°, with the ratio of ∠BAC, ∠ABC, and ∠ACB being 3 : 5 : 10. If the measure of ∠BAC is decreased by 10° and the measure of ∠ABC is increased by 10°, find the new ratio of the three angles.
3. In triangle ABC, the sum of the angles is 180°, and the ratio of ∠BAC, ∠ABC, and ∠ACB is 3 : 5 : 10. Calculate the new ratio of the angles if the measure of ∠BAC is reduced by 10° and the measure of ∠ABC is increased by 10°.