(i) Using componendo and dividend, find the value of x, when:


(ii)The total expense of a trip for certain number of people is ₹18000. If three more people join them, then the share of each reduces by ₹3000. Taking x to be the original number of people, form a quadratic equation in x and solve it to find the value of x.

(iii) Using ruler and compass only construct ∠ABC = 60°, AB = 6 cm and BC = 5 cm.
(a) construct the locus of points equidistant from AB and BC.
(b) construct the locus of points equidistant from A and B.
(c) Mark the point which satisfies both the conditions (a) and (b) as P.
Hence, construct a circle with centre P and passing through A and B.

Solution

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