Question

The ratio of the number of coins in boxes A and B was 17:7. After 108 coins were shifted from box A to box B, this ratio became 37:20. The number of coins that needs to be shifted further from A to B, to make this ratio 1:1, is

Hint:

For ratio problems with transfers between two containers, first express initial quantities with a variable using the given ratio, then use the new ratio after transfer to form an equation. Finally, use total quantity (which stays constant) to handle any further equalisation like making the ratio 1:1.

Answer 1

Correct Answer: 272

Step 1: Let initial coins be \( 17k \) (A) and \( 7k \) (B). After moving 108 coins from A to B: \( \frac{17k-108}{7k+108}=\frac{37}{20} \), which gives \( k=76 \).
Step 2: So A \( =1184 \), B \( =640 \) right after the first shift, with total coins \( =1824 \) fixed forever.
Step 3: For a \( 1:1 \) ratio, each box must hold \( 1824/2 = 912 \) coins. A currently holds 1184, which is 272 more than 912.
\[ \boxed{272 \text{ coins}} \]