Question

In a college, 15% of the students are daily passengers and 25% of the remaining live in the
hostel. If even after this the students left are 3,366, find the strength of that college.​

Answer 1

Answer:

$\huge \colorbox{pink}{SOLUTION}$

Given,

15% live in hostel .

25% of the remaining are passengers.

the rest of student left are = 3366.

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Let , x be the total strength of students.

Now,

0.15x + .25 × .85 × x + 3366 = x

Simplify to get,

0.15x + 0.2125x + 3366 = x

Now , combine like terms to get ,

0.3625x + 3366 = x

Subtract 0.3625x from both the side of eq. , we get

3366 = x - 0.3625x

=> 3366 = 0.6375x

Now , divide both the side of eq. by 0.6375 , we get

$\frac{3366}{0.6375} = x$

Solve for x , we get,

$x = \frac{3366}{0.6375} = 5280$

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NOW,

15% live in the hostel = 15×5280 = 792

25% are passengers = 0.2125× 5280 = 1122

3366 are left = 3366

=> 792+1122+3366= 5280

THEREFORE, THE TOTAL STRENGTH OF COLLEGE IS 5280 .

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