Question

a man bought some pens for 60 rupees if the price of each pen had been one rupees less he would have got three pen more how much did he each pen cost him in rupees originally.​

Answer 1

Answer:

Answer =15

Now calculation starts as,

As per the information given , if we decrease the cost per pencil by 1 then we can get more of 5 pencils, so

Taking a simple approach

We get a hint that it might be a number nearing 5, that is a cost for one pencil, so

60/5=12

And reducing amount per pencil by one,

60/4=15

Similarly ,

60/3=20

i.e, +5 than the previous number of pencils bought.

And volla, we have the answer is 15.

Step-by-step explanation:

Answer 2

Answer:

hey here is your solution

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Step-by-step explanation:

$so \: let \: the \: cost \: of \: each \: pen \: originally \: be \: x.rs \: and \: no \: of \: pens \: be \: y \\ so \: we \: know \: that \\ cost \: of \: any \: stuff = its \: initial \: cost \: \times \: quantity \: of \: stuff \\ = xy \\ \\ so \: according \: to \: first \: condition \\ xy = 60 \\ ie \: \: x = \frac{60}{y} \: \: \: \: \: \: \: \: \: (1)\\ \\ according \: to \: second \: condition \\ (x - 1)(y + 3) = 60 \\ xy + 3x - y - 3 = 60 \\ 60 + 3x - y - 3 = 60 \\ 3x - y - 3 = 0 \\ 3x - y = 3 \\ ie \: \: 3 \times \frac{60}{y} - y = 3 \: \: \: \: \: \: \: \: \: from \: (1)\\ \\ \frac{180}{y} - y = 3 \\ multiplying \: dividig \: throughout \: by \: y \: \\ we \: get \\ 180 - y {}^{2} = 3y \\ ie \: \: y {}^{2} + 3y - 180 = 0$

$so \: thus \: then \\ y {}^{2} + 1 5y - 12y - 180 \\ y(y + 15) - 12(y + 15) = 0 \\ (y + 15)(y - 12) = 0 \\ y + 15 = 0 \: \: \: or \: \: \: y - 12 = 0 \\ ie \: y = - 15 \: \: \: or \: \: y = 12 \\ \\ but \: as \: no \: of \: pencils \: is \: never \: negative \\ y = - 15 \: is \: absurd \\ hence \: y = 12$

$substitute \: value \: of \: y \: in \: (1) \\ we \: get \\ x = \frac{60}{y} \\ \\ = \frac{60}{12} \\ \\ = 5 \\ hence \: x = 5$

$thus \: original \: cost \: of \: pencil \: is \: rs.5$