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Question

The sum of three numbers is 212. If the ratio of he first to the second is 13:16 and that of he second to the third is 2:3, then find the numbers.
[Let the numbers be a a,b and c, then ab=1316 and bc=23=1624,
i.e,a:b:c=13:16:24.. Divide 212 in the ratio 13:16:24 to get the numbers.

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Solution

Let the numbers be a,b,c.
a+b+c=212 _____ 1st condition
ab=1316 bc=23 ..... (given)
a=13b16 c=3b2
substituting in eq (1)
13b16+b+3b2=212
b(1316+1+32)=212
b=64
a=13×b16=13×6416=52
c=3b2=3×642=96.
a=52
b=64
c=96.

1202628_1249470_ans_879f9d0f279740d3ab6245e723a0b5bc.jpg

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