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In a university, the ratio of B.Tech. Students to B. Sc. students is 2 : 5 and the ratio of M.Tech. Students to B.Sc. students is 1 : 3. If 10 new M.Tech. Students join the university, then how many more B. Tech. Students are required, so that the ratio among B.Tech., B.Sc. and M.Tech. Students becomes 1 : 1 : 1?

In a university, the ratio of B.Tech. Students to B. Sc. students is 2 : 5 and the ratio of M.Tech. Students to B.Sc. students is 1 : 3. If 10 new M.Tech. Students join the university, then how many more B. Tech. Students are required, so that the ratio among B.Tech., B.Sc. and M.Tech. Students becomes 1 : 1 : 1? Correct Answer 9

Given:

In a university, the ratio of B.Tech. Students to B. Sc. students is 2 : 5 and the ratio of M.Tech. Students to B.Sc. students is 1 : 3

Calculation:

Let x be B.Tech Students, y be B.Sc. Students and z be M.Tech. Students.

So, x : y = 2 : 5 and z  :  y = 1 : 3

On combining all the ratio

x : y : z = 6 : 15 : 5

If 10 new M. Tech. Students joined the university and no other joins, then above ratio becomes = x : y : z

Suppose x B.Tech. Students joined the university.

6 + x : 15 : 5 + 10

It will be 1 : 1 : 1, if 6 + x = 15

⇒ x = 9

Thus, 9 new B.Tech. Students are required.

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