NCERT Solutions Ganita Prakash (Part 2) Chapter 1 In-text Questions — — Tricky Percentages

Book page 26 Updated on2026-09-05

Q1.

A provision store is offering a stock clearance sale. Customers can choose one of the two options — 20% discount or ₹50 discount — for any purchase above ₹150. Which option would you choose if you want to: (i) buy items worth ₹180 (ii) buy items worth ₹225 (iii) buy items worth ₹300

Answer

Purchase	20% discount	₹50 discount	Better choice	You pay
(i) ₹180	₹36	₹50	₹50 off	₹130
(ii) ₹225	₹45	₹50	₹50 off	₹175
(iii) ₹300	₹60	₹50	20% off	₹240

The two offers are worth the same at one particular bill:

20% of x = 50
0.2x = 50 → x = ₹250

Why it happens: The ₹50 discount is a fixed amount — it does not grow with the bill. The 20% discount grows in step with the bill, so it is worth ₹30 on a ₹150 purchase and ₹60 on a ₹300 one. Below ₹250 the fixed discount is larger; above ₹250 the percentage discount overtakes it. Knowing the ₹250 break-even point lets you decide any bill at a glance, without working out both offers each time.

Q2.

A bakery called Cakely is offering a 30% + 20% discount on all cakes. Another bakery called Cakify is offering a 50% discount on all cakes. Would you rather choose Cakely or Cakify if you want the cheaper cost?

Answer

Cakify — its single 50% discount is genuinely bigger than Cakely's “30% + 20%”.

For a cake worth ₹200:
Cakely: 30% off ₹200 → 200 – 60 = ₹140
then 20% off ₹140 → 140 – 28 = ₹112

Cakify: 50% off ₹200 → ₹100

Cakely's offer is really a single discount of 44%, not 50%:

Price paid = 0.70 × 0.80 × MP = 0.56 × MP
So the customer pays 56% and the discount is 44%

Why it happens: In shopping, “30% + 20%” means the discounts are applied one after the other, and the second one is taken on the already reduced price — 20% of ₹140, not 20% of ₹200. Percentages taken in succession multiply their remaining fractions (0.7 × 0.8 = 0.56); they do not add their discounts. The missing 6% is precisely 20% of the first ₹60 discount — a discount you never get, because that ₹60 has already been taken off.

Tip: Order does not matter. 20% first and then 30% also gives 0.8 × 0.7 = 0.56, i.e. ₹112. What matters is that a reduced price becomes the base for the next reduction.

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