Two towns P and Q are 60 km apart. A school is to be built to serve 150 students in town P and 50 students in town Q. If the total distance to be travelled by 200 students is minimum, then the school should be built at

Town P

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Town Q

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45 kms from Town P

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45 kms from Town Q

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Solution

The correct option is A Town P
Given that PQ = 60 kms.
Let the school be at a distance of x kms from Town P (with 150 students). So, the distance of school from Town Q (with 50 students) will be (60 - x).
Then the distance travelled by 200 students is
D = 150x + 50 (60 - x) = 100x + 3000.
D will be least and equal to 3000 if x = 0, i.e., school is built at P.

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Q. Two towns P and Q are 60 km apart. A school is to be built to serve 150 students in town P and 50 students in town Q. If the total distance to be travelled by 200 students is minimum, then the school should be built at

Two towns $A$ and $B$ are $60 k m$ apart. A school is to be built to serve $150$ students in town $A$ and $50$ students in town $B$ . If the total distance to be travelled by all $200$ students is to be as small as possible, then the school should be built at