What is the total number of rejected sports shoes from all the companies…

Concept: a percentage always acts on its own base. When several groups each carry their own base and their own rate, their counts add group by group, so the combined count equals the sum of (base × rate ÷ 100) taken over all the groups. Applying one single percentage to a pooled base is valid only when every group carries the identical rate.

Application: for 2022 each company has its own output (in lakh) and its own rejection rate, so the rejected shoes of each company must be worked out separately as Number × Rejected(%) ÷ 100 lakh.

Adding the rejected column gives 0.75 + 1.30 + 0.64 + 2.16 + 1.40 + 0.90 + 1.20 = 8.35 lakh rejected shoes for 2022.

Cross-check by an independent route:

1. One lakh taken at 1% is exactly 1000 shoes, so the whole sum reduces to adding the plain Number × Rejected(%) products and multiplying by 1000.

2. Those products are 75, 130, 64, 216, 140, 90 and 120; they total 835.

3. 835 × 1000 shoes is 8.35 lakh, which matches the column total reached above.

A frequent slip is to average the seven rejection rates (3, 5, 2, 9, 4, 5, 4, giving about 4.57%) and apply that average to the pooled output of 190 lakh, which yields roughly 8.69 lakh. That treats a company producing 18 lakh as equal in weight to one producing 35 lakh; weighting each rate by its own output is exactly what the per-company sum does.

Result: one lakh is 100000, so the 2022 rejected total of 8.35 lakh works out to 8.35 × 100000 = 835000 sports shoes.