**The first mistake people do when they see a question on faulty instruments is that they get ready to use excessive brains! STOP there if you think that brain usage is a skill in the exam hall! Brain should be used before the exam begins – patterns understood and concepts captured. Let us begin the BRAINY GAME here.**

SAMPLE QUESTION 1: A dishonest shopkeeper used a faulty balance that balances when 11kg is one pan and 10kg is in the other. He sells after hiking the cost price of the product by 10%. If he cheats the farmer while buying and the buyer while selling through his faulty balance, find his actual gain percent in the whole transaction.

a. 33.1% b. 22% c. 22.22% d. 30%

- Now, while buying he will buy 11 in place of 10 => 11/10 in place of 1. =>

o If CP of 1 = Rs. 1, then his effective cost price can be found. How? See

§ 11 units for Rs. 10 => 1 unit for Rs. 10/11 => Cost price

- Now, while selling he will sell 10 in place of 11 => Unit selling price can be found.

o SP => He gets 11 in place of Rs. 10. Therefore, SP = 11/10

- Now, he hikes the cost price by 10% => SP => 11/10*11/10 = 121/100.

Now situation: CP = 10/11, SP = 121/100. Profit percentage now?

P% = [(SP/CP) – 1 ] * 100

= (121/100*11/10 – 1)*100 = (1.331-1)*100 = 33.1 %

**Now, lets understand the game:**

STEP 1: 11/10 in his favor

STEP 2: 11/10 through price hike

STEP 3: 11/10 in his favor

NET EFFECT => (11/10)^3 = 1.331 => 33.1%

How does confusion arise then? Let us take an example:

· A grain dealer cheats to the extent of 10% while buying as well as selling by using false weights. His total gain is?

- See, 10% gain, then 10% loss => 11/10*11/10 = 1.21 => 21% gain overall.

- Conceptually now, while selling he sells 10/11 per unit and while buying he buys 11/10 per unit as compared to norms. So,

- P% = [(SP/CP) – 1 ] * 100

- 11/10*(1/10/11) = 1.21. Hence 21% gain.

SAMPLE QUESTION 2: While using a meter scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on the cash payment, what is his overall profit percentage?

Solution:

While selling, he sells 8/10 per unit. While buying he buys 12/10 per unit.

Hence, total overall change => 12/10 * 10/8 * 4/5 = 1.2 => 20% gain.

Let me explain through one diagram now:

SAMPLE QUESTION 3: While using a meter scale, a cloth merchant uses a 110 cm scale while buying, but uses an 90 cm scale while selling the same cloth. If he offers a discount of 25% on the cash payment, what is his overall profit percentage?

Hope the above practice made you clear with the concept of a faulty balance. Will be back later with an article on faulty clocks. There are some short cuts on the balance thing in some texts; I do not recommend those formulas. Normally, should not be required.