Question

Narcisse and Aristide have numbers of arcade tokens in the ratio 7 : 3, respectively. Narcisse gives Aristide some of his tokens, and the new ratio is 6 : 5. What is the least number of tokens that Narcisse could have given to Aristide?a. 9b. 17c. 21d. 27e. 53

Answer 1

Narcisse could have given 17

Explanation:

Given that Narcisse and Aristide have numbers of arcade tokens in the ratio 7 : 3

Let Narcisse have 7x and Aristide 3x respectively

If d tokens are given from Narcisse to Aristide, new belongings

7x-d, 3x+d

Ratio is 6:5

`7x-d:3x+d=6:5\\35x-5d = 18x+6d\\11d = 17x`

i.e. So x should be a multiple of 11

least number of x =11

Verify:

Narcisse and Aristide have intially 77 and 33.

Narcisse gave 17 to Aristide

New are 60 and 50 making ratio 6:5

So answer is 17