A bag containing potatoes, onions and lemons weighs 46 kg 160 g. The weight of potatoes is 17 kg 115 g and that of onions is 15 kg 325 g. The weight of empty bag is 120 g. If 30 lemons weigh 1 kg, then what is the number of lemons in the bag?

To find the number of lemons in the bag, we first need to determine the total weight of the lemons. Let's break down the given weights and convert all of them into a single unit (grams) for easier calculations.
We know that $1\text{kg}=1000\text{g}$.

Step 1: Convert all given weights into grams:
Total weight of the bag containing potatoes, onions, and lemons:
$46\text{kg}160\text{g}=(46\times 1000)+160=46160\text{g}$

Weight of the potatoes:
$17\text{kg}115\text{g}=(17\times 1000)+115=17115\text{g}$

Weight of the onions:
$15\text{kg}325\text{g}=(15\times 1000)+325=15325\text{g}$

Weight of the empty bag:
$120\text{g}$

Step 2: Find the combined weight of the potatoes, onions, and the empty bag:
$\text{Combined Weight}=17115\text{g}+15325\text{g}+120\text{g}$
$\text{Combined Weight}=32560\text{g}$

Step 3: Calculate the total weight of the lemons:
The total weight of the loaded bag is the sum of the weights of the potatoes, onions, lemons, and the empty bag itself.
$\text{Weight of lemons}=\text{Total weight}-\text{Combined weight of other components}$
$\text{Weight of lemons}=46160\text{g}-32560\text{g}=13600\text{g}$
Converting this back to kilograms:
$13600\text{g}=13.6\text{kg}$

Step 4: Find the total number of lemons:
We are given that 30 lemons weigh 1 kg. Thus, the number of lemons per kg is 30.
$\text{Number of lemons}=\text{Weight of lemons in kg}\times 30$
$\text{Number of lemons}=13.6\times 30=408$

Therefore, the number of lemons in the bag is 408.