A person has four boxes of different integral but unknown weights. The person weighted the boxes in triplets. He obtained the weights in kgs as 150, 170, 180, 190. How much would the heaviest box weigh? (in kgs)
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Given:
The weights of boxes weighed in triplets in kgs is 150, 170, 180, 190 kg.
To Find:
The weight of the heaviest box.
Calculation:
- Let the weight of the boxes be a, b, c and d kgs.
- According to the question:
a + b + c = 150 ...(i)
b + c + d = 170 ...(ii)
a + c + d = 180 ...(iii)
a + b + d = 190 ...(iv)
(i) + (ii) ⇒ 2(b + c) + (a + d) = 320 ...(v)
(iii) + (iv) ⇒ 2(a + d) + (b + c) = 370
⇒ (b + c) = 370 - 2(a + d)
- Putting this in (v), we get:
2{370 - 2(a + d)} + (a + d) = 320
⇒ 740 - 4(a + d) + (a + d) = 320
⇒ 3 (a + d) = 420
⇒ (a + d) = 140 ...(vi)
- From (iii) and (vi), we get:
c + 140 = 180
⇒ c = 40
- From (iv) and (vi), we get:
b + 140 = 190
⇒ b = 50
- From (i), we have:
a + 50 + 40 = 150
⇒ a = 60
- From (ii), we have:
50 + 40 + d = 170
⇒ d = 80
- So, the weight of the heaviest box is 80 kg.
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