Question

A shop sold 64 kettles of two different capacities. The smaller kettle cost a rouble less than the larger one. The shop made 100 roubles from the sale of large kettles and 36 roubles from the sale of small ones. How many kettles of each capacity did the shop sold and what was the price of each kettle?

Answer 1

Suppose shop make a number of small cattle and A number of large cattle and rate of large cattle is $(t+1)$ and rate of small cattle is t.

So, $a+A=64$ (given)

$a\times t=36$

$A(t+1)=100$

$\Rightarrow At+A=100$

$+at=36$

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$(A+a)t+A=136$

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$(\because A+a=64)$

$64t+A=136$

$\Rightarrow \frac{136-A}{64}$

So, $A\frac{(136-A)}{64}+A=100$

$136A-A^2+64A=6400$

$\Rightarrow A^2-200A+6400=0$

$A=\frac{200\pm \sqrt{40000-6400\times 4}}{2}$

$A=\frac{200\pm 120}{2}$

$40,160$ (not possible above $64$)

So $a=64-40=24$ cattle.