Question

X and Y are two numbers. Two-third of the sum of 12% of X and 16% of Y is equal to the sum of 10% of X and 8% of Y. Determine the ratio of X and Y. *

1:1

3:4

2:3

4:3

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Answer 1

It has given that, X and Y are two numbers such that 2/3 rd of the sum of 12% of X and 16% of Y is equal to the sum of 10% of X and 8% of Y.

we have to determine the ratio of X and Y.

solution : step 1 : 2/3rd of the sum of 12% of X and 16% Y

= 2/3(12% of X + 16% of Y)

= 2/3(12X/100 + 16Y/100)

= 2/3(12x + 16Y)/100

= (12X + 16Y)/150

step 2 : the sum of 10% of X and 8% of Y.

= (10% of X + 8% of Y)

= 10X/100 + 8Y/100

= (10X + 8Y)/100

step 3 : 2/3rd of the sum of 12% of X and 16% Y = the sum of 10% of X and 8% of Y

⇒(12X + 16Y)/150 = (10X + 8Y)/100

⇒2(12X + 16Y) = 3(10X + 8Y)

⇒24X + 32Y = 30X + 24Y

⇒32Y - 24Y = 30X - 24X

⇒8Y = 6X

⇒X/Y = 4/3

Therefore the ratio of X and Y is 4 : 3