increase 5200 kg in the ratio $$ 2: 5 $$

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We are given that 5200 kg is to be increased so that the ratio of the original weight to the new (increased) weight is 2:5. In other words, after increasing, the relationship is

(original weight) : (new weight) = 2 : 5.

Let the required increase be x kg. Then the new weight becomes

5200 + x kg.

According to the ratio given, we have

5200 / (5200 + x) = 2 / 5.

Now, solve for x:

Step 1. Cross multiply:
  5200 × 5 = 2 × (5200 + x)
  26000 = 10400 + 2x

Step 2. Isolate x:
  26000 − 10400 = 2x
  15600 = 2x
  x = 15600 / 2
  x = 7800

Thus, the weight should be increased by 7800 kg.

Step 3. Check (optional):
The new weight is 5200 + 7800 = 13000 kg. The ratio of original to new weight is 5200 : 13000. Simplify by dividing both parts by 2600:
  5200 ÷ 2600 = 2 and 13000 ÷ 2600 = 5.
This confirms the ratio is 2:5.

Final Answer:
Increase 5200 kg by 7800 kg to obtain a new weight of 13000 kg, which is in the ratio 2:5 to the original weight.
Increase 5200 kg by 7800 kg to get a new weight of 13000 kg, maintaining a 2:5 ratio.

increase 5200 kg in the ratio \( 2: 5 \)

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