Question

solve for x and y
105x + 107y = 116700
107x + 105y = 116500​

Answer 1

Let the cost price of A is Rs. x and same of B is Rs. y

Then by the given question,

(x+x×5/100)+(y+y×7/100)=1167

or,( x+x/20)+(y+7y/100)=1167

or, 21x/20+107y/100=1167

or, 105x+107y=116700 --------------(1) and

(x+x×7/100)+(y+y×5/100)=1165

or, (x+7x/100)+(y+y /20)=1165

or, 107x/100+21y/20=1165

or, 107x+105y=116500---------------(2)

Multiplying (1) with 107 and (2) with 105 we get,

11235x+11449y=12486900 ---------------(3)

11235x+11025y=12232500 ---------------(4)

Subtracting (4) from (3) we get,

424y=254400

or, y=254400/424

or, y=600

Putting in (1) we get,

105x+107×600=116700

or, 105x=116700-64200

or, 105x=52500

or, x=52500/105

or, x=500

∴, Cost price of A is Rs. 500 and cost price of B is Rs. 600