a) 3
b) 6
c) 8
d) 9
Answer: a
Explanation: Clearly, A invested his capital for 12 months
while each one of B and C invested his capital for (12 – x) months
Ratio of profits os A, B, C
$$ = \left( {50000 \times 12} \right)$$ : $$\left[ {60000 \times \left( {12 – x} \right)} \right]$$ : $$\left[ {70000 \times \left( {12 – x} \right)} \right]$$
$$\eqalign{
& = 60:6\left( {12 – x} \right):7\left( {12 – x} \right) \cr
& {\text{But ratio of profits}} \cr
& = 20:18:21 \cr
& = 60:54:63 \cr} $$
$$ 60:\left( {72 – 6x} \right):\left( {84 – 7x} \right)$$ = $$60$$ : $$54$$ : $$63$$
$$\eqalign{
& {\text{So, }}72 – 6x = 54 \cr
& 6x = 18 \cr
& x = 3 \cr} $$
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