7.2.1. Estimation in percentages

Your bill in a shop is ₹577.80 and the shopkeeper gives a discount of 15%. How would you estimate the amount to be paid?

(i) Round off the bill to the nearest tens of ₹577.80, i.e., to ₹580.

To estimate the bill, the first step is to simplify the number by rounding it. Rounding off means changing a number to a simpler value that is approximately close to the original value. In this case, ₹577.80 rounds to ₹580 because we are looking at the nearest ten. When the number after the tens place (7 in this case) is 5 or more, we round up, and if it's less than 5, we round down.

Think of rounding off like estimating the time it takes to bake a cake. If the recipe says it takes 37 minutes, you might tell your friends it takes about 40 minutes instead. It's an easy way to communicate and gives a good idea of how long it will take.

(ii) Find 10% of this, i.e., ₹580 × 10% = ₹58.

Now that we have rounded the bill to ₹580, we calculate 10% of this amount to estimate the discount. To find 10% of a number, you can simply divide that number by 10. In this case, ₹580 divided by 10 equals ₹58. This value gives us a rough idea of how much discount we will receive.

Imagine you want to give a 10% tip at a restaurant. If your meal cost ₹580, calculating 10% is like slicing a piece of cake—you get a small portion, which in this case is ₹58. It makes deciding how much to tip easier.

(iii) Take half of this, i.e., ₹58 ÷ 2 = ₹29.

Next, we take half of the 10% amount calculated. This is because to find a 15% discount, you can think of it as 10% plus half of 10%. Hence, taking half of ₹58 gives us ₹29. This step helps us to get a clearer understanding of what a 15% discount approximately looks like.

If you have 58 marbles and you want to share them evenly with your friend, you would be giving away half, which is 29 marbles. This sharing concept helps visualize how we are just splitting the 10% discount for 15%.

(iv) Add the amounts in (ii) and (iii) to get ₹87.

We now need to combine the amounts we've calculated: the 10% discount of ₹58 and half of that amount, ₹29. Adding these values together gives us ₹87. This value represents an estimated discount on the original bill due to the shopkeeper's provided percentage discount.

Consider planning a party and needing supplies. If you estimate that balloons cost ₹58 and streamers cost ₹29, calculating the total you need to spend helps you better prepare your budget, just like estimating your discount total.

You could therefore reduce your bill amount by ₹87 or by about ₹85, which will be ₹495 approximately.

To determine the final estimated amount to pay, we subtract the estimated discount of ₹87 from the rounded bill amount of ₹580. This means you would expect to pay approximately ₹495 after applying the discount, even though the exact amount may differ slightly.

Imagine you're shopping for new shoes priced at ₹580 but find out there's a promise of savings. You can estimate how much you’ll actually part with—like planning for a trip where you've saved some money for expenses, which brings your final costs down.

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