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In a zoo there are tigers and ducks. When total heads were counted they were 338 and when total legs were counted it turned out to be 1052. Find the ratio of numbers of ducks to tigers.

In a zoo there are tigers and ducks. When total heads were counted they were 338 and when total legs were counted it turned out to be 1052. Find the ratio of numbers of ducks to tigers. Correct Answer 75 ∶ 94

GIVEN :

Total number of animals = 338

Total legs count of animals = 1052

 

CONCEPT :

Ratio method

 

ASSUMPTION :

Let the number of tigers be t & number of ducks be d.

 

CALCULATION :

∴ t + d = 338      ---- (1)

As we know tigers have 4 legs while ducks have 2.

∴ Total leg counts = leg count of tigers + leg count of ducks

∴ 1052 = 4t + 2d

∴ 2t + d = 526      ---- (2)

Subtracting equation 1 from equation 2-

t = 188

∴ substituting the value of t in equation 1-

∴ d = 150

∴ Ratio of number of ducks to tiger = 150 ∶ 188 = 75 ∶ 94

∴ Answer is 75 ∶ 94

 

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