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

Entered answer:

✅ Correct Answer: 272

Let the common multiplier be $x$ .

Initially, Box A has $17x$ coins and Box B has $7x$ coins.

After shifting 108 coins from A to B:

Box A $= 17x - 108$

Box B $= 7x + 108$

The new ratio is $37 : 20$ , so:

$\dfrac{17x - 108}{7x + 108} = \dfrac{37}{20}$

$20(17x - 108) = 37(7x + 108)$

$340x - 2160 = 259x + 3996$

$340x - 259x = 3996 + 2160$

$81x = 6156$

$x = 76$

Box A (after shifting 108) $= 17(76) - 108 = 1292 - 108 = 1184$

Box B (after shifting 108) $= 7(76) + 108 = 532 + 108 = 640$

Total coins $= 1184 + 640 = 1824$

For the ratio to become $1 : 1$ , both boxes must have equal coins.

Each box should have $= \dfrac{1824}{2} = 912$ coins

Additional coins to shift from A to B $= 1184 - 912 = 272$

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