A jeweler has bars of 18carat gold and 12 carat gold How much of each must be melted together to obt...

Question

A jeweler has bars of 18carat gold and 12 carat gold How much of each must be melted together to obtain a bar of 16carat gold weighing 120 grams Pure gold is 24 carat

Accepted Answer

Lets assume the quantity of 18carat gold as x gm and 12carat gold as y gm Then according to the first condition given in the problem we have x y 120 i Pure gold is 24 carat So the purity of 18carat gold 1824 x 100 x 100 75 Purity of 12 carat gold 1224 x 100 x 100 50 And the purity of 16carat gold 1624 x 100 23 x 100 2003 Now according to the second condition given in the problem we have 75x 50y 2003 x 120 75x 50y 200 x 40 75x 50y 8000 3x 2y 320 ii Performing ii 2 x i we get 3x 2y 320 2x 2y 240 x 80 On substituting the value of x in equation i we get 80 y 120 y 120 80 y 40 Therefore the jeweler requires 80 gm of 18carat gold and 40 gm of 12carat gold to obtain a bar of 16 carat gold weighing 120 gm

ML Aggarwal Solutions Class 9 Mathematics Solutions for Problems on Simultaneous Linear Equations Exercise 6 in Chapter 6 - Problems on Simultaneous Linear Equations