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Parwez (V.P.) has some cocks and goats. If the total numbers of heads and feet are 76 and 212 respectively, then find the number of cocks he has.

(a) 76

(b) 16

(c) 46

(d) 64

Solution

Let the number of cocks $=x$

$\&$ the number of goats $=y$

$\therefore$ From the question,

$x+y=76$

$2 x+4 y=212$

$\therefore \quad$ We get after solving eqn. (i) and (ii), $x=46$, and $y=30$.

$\therefore$ Total no. of cocks $=46$; Ans.

$\therefore \quad$ Correct option is $(c)$

Trick : Suppose that the all heads are of goat.

$\therefore \quad$ Number of legs $=76 \times 4=304$

Difference of their feet

$=304-212=92$

The difference of their feet

$=4-2=2$

No. of cocks $=\frac{92}{2}=46 ;$ Ans.

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