Question

A tiara is studded with a mixture of gems. The ratio of sapphires to emeralds is 3:1. If 6 emeralds are added, the tiara will contain an equal number of sapphires and emeralds. How many emeralds must be added to the original tiara so that the ratio between emeralds and sapphires is 3:1?

(A) 9
(B) 12
(C) 18
(D) 24
(E) 27

Answer 1

Answer: Option 'A' is correct.

Explanation:

Since we have given that

Ratio of sapphires to emeralds = 3:1

Let the number of sapphires be 3x.

Let the number of emeralds be 'x'.

According to question, if 6 emeralds are added, we get that

`3x=x+6\\\\3x-x=6\\\\2x=6\\\\x=(6)/(2)\\\\x=3`

So, Number of sapphires = 3×3 = 9

Number of emeralds = 3

So, total emeralds would be 3+ 6 = 9.

Hence, option 'A' is correct.