Man and Horse

Algebra Level 2

One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he counted 74 heads and 196 legs. How many humans and horses were there?

24 horses and 50 humans 37 humans and 98 horses 31 horses and 46 humans 46 horses and 31 humans

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3 solutions

Kay Xspre
Jan 28, 2016

If all men and horse has two legs, there will be only 74 × 2 = 148 74\times2 = 148 legs, but provided the horse have four legs, the sum of all legs shall also take account the two legs increasing per each horse, hence there are 196 148 2 = 24 \displaystyle\frac{196-148}{2} = 24 horses and 50 men.

Nice \large\text{Nice}

Rishabh Jain - 5 years, 4 months ago
Mohammad Khaza
Jul 18, 2017

very good question. but very easy/unthinking options.

only in option 1 there is 74 heads and the other options have more heads .

so, i don't need to do the math. just to look at the option 1.

so, option 1 is the answer.

i too got that.

Halima Tahmina - 3 years, 11 months ago

let H H be the number of horses and P P be the number of humans

since a horse has four feet and a human has two feet, we have the two equations

H + P = 74 H+P=74 ( 1 ) \color{#D61F06}(1)

4 H + 2 P = 196 4H+2P=196 ( 2 ) \color{#D61F06}(2)

Solving H H in ( 1 ) \color{#D61F06}(1) , we get H = 74 P H=74-P . Substituting this in ( 2 ) \color{#D61F06}(2) , we have

4 ( 74 P ) + 2 P = 196 4(74-P)+2P=196

296 4 P + 2 P = 196 296-4P+2P=196

100 = 2 P 100=2P

50 = P 50=P

It follows that H = 74 50 = 24 H=74-50=24 .

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