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The ratio between the number of gold medals and silver medals in a box is 13 : 16. If 10 gold medals are lost and 8 silver medals are found and included with the other medals in the box, then the ratio becomes 4 : 10. After the losing and finding, what is the difference between the total number of silver medals and number of gold medals.

The ratio between the number of gold medals and silver medals in a box is 13 : 16. If 10 gold medals are lost and 8 silver medals are found and included with the other medals in the box, then the ratio becomes 4 : 10. After the losing and finding, what is the difference between the total number of silver medals and number of gold medals. Correct Answer 24

Let number of gold medals and number of silver medals be M: N respectively.

Given:

⇒ M : N = 13 : 16

⇒ M/N = 13/16

After losing and finding,

⇒ (M – 10): (N + 8) = 4 : 10

⇒ 10M – 100 = 4N + 32

⇒ 10M – 4N = 132

⇒ 10(13N/16) – 4N = 132

⇒ N = 32

⇒ M = 26

Required difference in number of medals =

= (32 + 8) – (26 – 10)

= 24

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