Question 64

Modi, Trump and Abe are involved in in a project manufacturing nuclear bombs to attack China. They are manufacturing some bombs individually and some in groups of two and all the three together are manufacturing some bombs. The total bombs being manufactured is sixteen time the number of bombs being prepared by all the three together. The number of bombs that Modi and Trump are manufacturing together without Abe is 6. Trump is manufacturing 11 bombs all by himself. Abe is manufacturing 8 bombs by himself. Modi is manufacturing 7 bombs by himself. 22 bombs are being manufactured by atleast two of them together. Modi is involved in the manufacturing of 20 bombs. How many bombs are Abe and Trump manufacturing together without involving Modi?

Solution

Only Trump is 11
Only Abe is 8
and only Modi is 7
atleast two are invloved in the manufacture of 22 bombs.

So, the total bombs being manufactured = 11 + 8 + 7 + 22 = 48

So, the number of bombs being manufactured by all three together = 48/16 = 3

The number of bombs that Modi and Trump are manufacturing together without Abe is 6.
So, number of bombs that Modi and Abe are preparing without Trump = 20 - 7 - 3 -6 = 4

So, the number of bombs that Abe and Trump are manufacturing together without Modi = 48 - 11 - 8 - 7 - 4 - 6- 3 = 9

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