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A computer program was tested 300 times before its release. The testing was done in three stages
of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only?
Let the software fails $$a, b$$ and $$c$$ times in a single stage, in two stage and in all stages respectively.
Given : $$c = 4$$
To find : $$a = ?$$
Solution : $$a + 2b + 3c = 15 + 12 + 8$$
=> $$a + 2b + 3c = 35$$ -------------Eqn(I)
Also, $$b + 3c = 6 + 7 + 4$$
=> $$b + (3 \times 4) = 17$$
=> $$b = 17 - 12 = 5$$
Using eqn(I),
=> $$a + (2 \times 5) + (3 \times 4) = 35$$
=> $$a + 10 + 12 = 35$$
=> $$a = 35 - 22 = 13$$
