Multiple choice general knowledge math & puzzles

If a:b=c:d Then, (pa+qc)/(pb+qd) will be

  1. p:q

  2. a:b

  3. c:d

  4. a:b and c:d
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If a:b = c:d = k (say), then a = bk and c = dk. Substituting in (pa+qc)/(pb+qd) gives (pbk+qdk)/(pb+qd) = k(pb+qd)/(pb+qd) = k = a/b = c/d. The expression simplifies to the original ratio, so both a:b and c:d are equivalent answers. Option D correctly captures this.

AI explanation

To solve this question, let's start by understanding the given equation:

a:b = c:d

This equation represents a proportion, where the ratio of a to b is equal to the ratio of c to d.

Now, let's consider the expression (pa+qc)/(pb+qd). We can simplify this expression by multiplying both the numerator and denominator by the same value.

Multiplying the numerator by p and the denominator by q, we get:

(pa+qc)/(pb+qd) = (p*a + q*c)/(p*b + q*d)

Now, let's compare this expression to the given equation a:b = c:d.

The numerator of the expression (pa+qc)/(pb+qd) is p*a + q*c, which has the same ratio as a and c.

The denominator of the expression (pa+qc)/(pb+qd) is p*b + q*d, which has the same ratio as b and d.

Therefore, the expression (pa+qc)/(pb+qd) has the same ratio as a:b and c:d.

Hence, the correct answer is option D) a:b and c:d.

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