Question

Two metals X and Y are to be used for making two different alloys. If the ratio by weight of X : Y in the first alloy is 6 : 5 and that in the second is 7 : 13, how many kg of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second so as to produce a new alloy containing 40% of metal Y?

Answer 1

11 kg of 1st alloy + 20 kg of 2nd alloy
= {(11×6)+(7×20)} : {(5×11)+(13×20)}
= (206 : 315)

new alloy should contain only 40 % of y and the % is more so we need to add extra x metal

here
Y = 315kg ( which should be 40 %)
hence total metal must be
= (315×100)/40
=787.5 kg
hence,
the extra amount of x metal
= 787.5 - 206 - 315
= 266.5 kg