Question

The profit in rupees in a local restaurant and the number of customers who visited the restaurant are tabulated below for each week for one month.

Week number	Week 1	Week 2	Week 3	Week 4
Number of customers	1400	5600	x	3212
Profit in ₹	28000	112000	32140	y

Find:

1. if the number of customers and profit per week in continued proportion or not? Justify your answer.
2. the value of x and y.

Answer 1

Given:

Week 1: customers = 1400, profit = ₹ 28000.

Week 2: customers = 5600, profit = ₹ 112000.

Week 3: customers = x, profit = ₹ 32140.

Week 4: customers = 3212, profit = y. 

1. Check whether the sequences are in continued proportion.

For a sequence to be in continued proportion, successive ratios must be equal, i.e. for customers:

1400 : 5600 = 5600 : x = x : 3212

`1400 : 5600 = 1400/5600` = `1/4`

If they were continued in proportion, `5600/x` must equal `1/4`

⇒ `x = 5600 ÷ 1/4`

= 5600 × 4

= 22400

But using the profit data see step 2 we get a different x (1607). 

Therefore, the number-of-customers sequence is NOT in continued proportion.

Similarly for the profit sequence: `28000 : 112000 = 1/4` but the next given profit is 32140 not `112000 xx 1/4`, so the profit sequence is also NOT in continued proportion.

Conclusion on continued proportion: the sequences are not continued in proportion.

2. Use direct proportionality profit ∝ number of customers to find x and y.

Profit per customer from Week 1

= 28000 ÷ 1400

= ₹ 20 per customer

Check Week 2: 112000 ÷ 5600 = ₹ 20

So, profit is directly proportional to customers with constant ₹ 20/customer.

Week 3: x = profit ÷ (profit per customer)

= 32140 ÷ 20

= 1607

Week 4: y = customers × (profit per customer)

= 3212 × 20

= 64240