Question

the average price of 15 bolts and 10 nuts is rs.16. if the average price of 10 bolts and 15 nuts is rs.14. find the price of bolt?

Answer 1

$\text{Let x and y be the price one bolt and one nut respectively}$

$\boxed{\textbf{Average =\frac{\text{Sum of observations}}{\text{Number of observation}} }}$

$\text{As per given data, we have}$

$\frac{15x+10y}{25}=16$ and

$\frac{10x+15y}{25}=14$

$\implies$

$15x+10y=400$........(1)

$10x+15y=350$........(2)

$\text{Adding(1) and (2), we get}$

$25x+25y=750$

$\implies\,x+y=30$......(3)

$\text{Subtracting(2) from (1), we get}$

$5x-5y=50$

$\implies\,x-y=10$........(4)

$\text{Adding(3) and (4), we get}$

$2x=40$

$\implies\,\boxed{\bf\,x=20}$

$\therefore\,\textbf{Price of one bolt is Rs.\,20}$