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In a housing colony, the number of people who use public transportation options is 75% of the total colony population also no [person uses more than one mode of transportation. Only three modes of public transportation available in the city, Bus, Metro and Cab. If the number of people using bus is 25% more than the number of people using metro and the number of people using cab for public transportation is 25% less than the number of people using metro. What percentage of the total colony population using Metro?
1. 25
2. 50
3. 33.33
4. 42.15

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Correct Answer - Option 1 : 25

Let M = number of people using the metro.

      C = number of people using cab.

      B = number of people using bus.

      T = Total population.

Given that

\(\frac{B-M}{M}\times100 =25\)

\(\frac{B-M}{M} =\frac{25}{100}=\frac{1}{4}\)

\(4(B-M)=M\)

\(B=1.25M\)                                      ---(1)

Similarly,  

\(\frac{M-C}{M}\times100 =25\)

\(C=0.75M\)                                      ---(2)

No person uses more than one transport option also, people using public transportation is 75% of the total colony population.

\(\therefore C+B+M=0.75T\)                       ---(3)

Putting equations (1) and (2)  in (3).

\(0.75M+1.25M+M=0.75T\)

\(3M=0.75T\)

\(M=0.25T\)                                   ---(4)

From equation (4), we can say that number of people using metro is  25% of the total population.

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