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Question

Let A=2^i+7^j,B=^i+2^j+4^k, C=9^i+30^j+4^k5.

The ratio in which C divides AB internally is?

A
1:4
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B
2:3
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C
3:2
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D
5:1
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Solution

The correct option is B 1:4
As shown in the figure let C divide AB in a ratio K:1
So C=KB+AK+1
9^i+30^j+4^k5=K(^i+2^j+4^k)+(2^i+7^j)K+1
9K^i+30K^j+4K^k+9^i+30^j+4^k=5K^i+10K^j+20K^k+10^i+35^j
4K^i+20K^j16K^k=^i+5^j4^k
4K(^i+5^j4^k)=^i+5^j4^k
K=14
Hence, C divide AB in a ratio 1:4

55249_35578_ans_a6a8fb45e97a4b4bbffeca910fcc9eff.png

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