a and b together do a work in 20 days. b and c together in 15 days and c and a in 12 days. so a, b and c together finish same work in how many days?  Choose the correct choice from the following choices:
A) 12	B) 15	C) 8	D) 10	E) 11
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/20) + (1/15)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">(1/12) + (7/60)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) / 2</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 / (1/10)</gadget>
<output>10</output>

<result>D</result>
a and b together do a work in 20 days. b and c together in 15 days and c and a in 12 days. so a, b and c together finish same work in how many days?
inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2))
( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 so , all three together finish work in 10 days answer d