Question

a shopkeeper has a weighing balance containing two iron plates on both sides.

but this weighing balance is defective.

one plate is 10 % shorter than the another one

he sells apples for rs 27 per kg

he puts 1 kg bar on the smaller plate and apples on the other side.

Determine the cost price of the apples for the shopkeeper when he faces neither gain nor loss on this transaction.

Answer 1

We need the weight of the Iron plate - either the defective one or good one.

If the weight of good plate is 1 Kg and defective is 0.9  kg  (10% less).  Then
Apples sold will actually weigh only  0.9 Kg when balanced.  But shopkeeper charges for 1 Kg apples.

Gain of shopkeeper on selling 1 kg    ---- he gains  ---- 0.1 kg 
           =>  Rs 27 / Kg * 0.1 Kg             =    Rs 2.70
If the cost price of apples is higher by Rs 2.70  THen shopkeeper makes no profit or no loss.
So cost price of apples = Rs 27 + 2.70 = Rs 29.70 / Kg

IF THE WEIGHT OF GOOD plate is 2 Kg, then defective plate weighs 1.8 Kg only. Sold apples will weigh only 0.800 kg when a buyer wants 1 Kg.  So then Shopkeeper stands to gain 200 gm worth of apples => 0.200 * 27 = Rs 5.4
Then Cost price to even out profit or loss - no gain no loss =
        =  Rs 27 + 5.4 = Rs 32.4