weights and measures

The spring balance of a trader shows 800 grams for 1 kg. What is the net result, a profit or loss and by what percentage?










Answer
The trader looses 200 gms on selling 1000 gms of material.

So, by selling 1000 gms he looses 200 grams

therefore by selling 100 gms he will loose = (200/1000) x 100 = 20 % loss.

Percentage (4)

30% income of P is equal to 1.5% income of Q and 10% income of Q is equal to 20% income of R. If the income of R is Rs 4000; then the total income of P, Q and R is ..................










Answer

(30/100)P = (1.5/100)Q -----------(1)

(10/100)Q = (20/100)R  -----------(2)

multiply (2) by 0 .15.

(1.5/100)Q = (3/100)R ------------(3)

compare (1) and (3), we have

(30/100)P = (1.5/100)Q = (3/100)R

But R = 4000

So, Q = (3/1.5)R = 2 x 4000 = 8000

P = (3/30) x R = (3/30) x 4000 = 400

So, P + Q + R = 400 + 8000 + 4000 = 12400

Percentage 3

The price of petrol increased by 25% and so a person reduced his consumption by 25%. What percentage is the rise or fall in the expenditure incurred by him on petrol?





Answer

Basis: 100 litres of petrol at Rs P per litre.

Initial expenditure = 100P

reduction in consumption: (1-.25) x 100 = 75 litres

current price of 75 litres = 75 x 1.25 x P = 93.75 P

Reduction in expenditure = 100P - 93.75P = 6.25P.

% reduction  in expenditure= (6.25P/ 100P) x 100 = 6.25%

percentage (2)

If the numerator of a fraction is decreased by 40% and the denominator is increased by 100%, the new value is 1. What was the original fraction?

Answer

Let the original fraction be X/Y
So, the new fractions is 
(1 - 0.4)X/ 2Y = 1
or 0.6 X / 2Y = 1
or X/Y = 1 x 2/0.6 
or X/Y = 20/6

Percentage

If X's income is 25% more than Y's and Y's income is 20% more than Z's, then by what percentage is X's income more than Z's?

Answer
Method 1

Let Y's income be 100.
So, X's income = 125.
Also given that
if Z's income is 100, then Y's income is 120

Let us follow the unitary method
when Y's income is 120, then Z's income is 100.
when Y's income is 100, then Z's income is (100/120) x 100 = 10000/ 120

Now when Z's income is (10000/120), then X's income is 125
So, when Z's income is 100, then X's income = 125 x (120/ 10000) * 100  = 150
So, X's income is 50% more than Z's.

method 2

1.25Y = X, ---------(1)
Y =1.2 Z -----------(2)
substituting (2) in (1), we have
1.25 x 1.2 Z = X
1.50 Z = X
So, X's income is 50% more than Z's income

measurement (3)

If the sides of a cuboid is increased by 20%. by what percentage does the volume increase?

Let the sides of cuboid be "a" , "b" and "c"

So, volume of cuboid = a x b x c --------------(1)

if the sides are increase by 20%, then the new sides are:

1.2a , 1.2b and 1.2c

So, new volume = 1.2 x a x 1.2 x b  x 1.2 x c = 1.728 abc  ------------(2)

increase = (1.728 - 1) abc

therefore % increase in the volume = 100 x (1.728 - 1)abc/abc = 72.8%

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