Ratio

Algebra Level 2

If A : B = 2 : 3 , B : C = 5 : 7 A:B=2:3, B:C=5:7 and C : D = 3 : 10 C:D=3:10 , then find the value of A : D A:D .

If the ratio can be written in the form X : Y X:Y , where X X and Y Y are coprime positive integers, submit the answer as X + Y X+Y .


The answer is 8.

Harshit Verma by Harshit Verma , 23, India

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3 solutions

A B \frac{A}{B} = 2 3 \frac{2}{3} , B C \frac{B}{C} = 5 7 \frac{5}{7} , C D \frac{C}{D} = 3 10 \frac{3}{10}

A B \frac{A}{B} B C \frac{B}{C} C D \frac{C}{D} = 2 3 \frac{2}{3} 5 7 \frac{5}{7} 3 10 \frac{3}{10} = 1 7 \frac{1}{7}

X Y \frac{X}{Y} = 1 7 \frac{1}{7}

so, x=1 and x=7

X+Y = 1+7 = 8

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Shivam Mishra
Feb 14, 2016

Just multiply all the given ratios to obtain A:D as all other terms cancel out.Hence,we obtain A:D as 1:7 .Therefore,the answer is 1+7=8

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Harshit Verma
Feb 14, 2016

A:B=2:3 then 3A=2B ---(1) B:C=5:7 then B=7/5C ---(2) C:D=3:10 then C=3/10D ---(3) By solving 1,2&3 we get A:D=1:7 So, x=1&y=7 X+Y=8

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