profit and loss

By selling 55 m of thread the shopkeeper gains the selling price of 22m. Find the gain percentage?








Answer:

Selling price of a meter of thread = y
so, selling price of 55m = 55y
and selling price of 22m = 22y
gain made by the shopkeeper on selling 55m of thread = 22y
cost price of 55m = 55y -22y = 33y
gain % = (gain/Cost price) x 100 = (22y/33y) x 100 = 66.67%

profit and loss

A man buys oranges at the rate of 6 for $2 and sells the whole lot at the rate of 7 for $3. In this process he gains $20. How many oranges did he purchase?






Answer
Selling price of 6 oranges = 3 x 6/7 = 18/7
gain on selling 6 oranges = (18/7) - 2 = 4/7
So, gain on selling 1 orange = (4/7)/6 = 4/42 = 2/21
Total gain = $20
so, no. of oranges purchased = 20/ (2/21) = 20 x 21/2 =210.

Profit and loss

The cost price of 16 articles is equal to the selling price of 12 articles. What is the gain or loss %?






Answer:

By selling 12 articles the shopkeeper gains 4 articles.
So, by selling 100 articles the shopkeeper will gain = (4/12) x 100 = 33.33 %

profit and loss

A vendor loses the selling price of 5 mangoes on selling 20 mangoes. His loss percentage is ......................




method 1
Selling price of 1 mango = y
so, selling price of 5 mangoes = 5y
and selling price of 20 mangoes = 20y
cost price of 20 mangoes = 20y + 5y = 25y
loss percentage = 100 x (loss/ cost price) = 100 x 5y/25y = 20%

5-time and work

A, B and C can complete a work, working alone in 10, 15 and 20 days respectively. If all three work together, what fraction of the work is done by B?

4-time and work

A is thrice as good a workman as B, and takes 60 days less than B for doing a job. Find the time in which they can do it together?

3-time and work

Taps A and B can fill a tank in 12 mins and 15 mins respectively. If both are opened and A is closed after 3 mins, how long will it take for B to fill the tank?

2-time and work

A sum of money is sufficient to pay A's wages for 21 days and B's wages for 20 days. For how many days is the fund sufficient to pay the wages when both are working together?

1-Time and work

A can do a certain job in 12 days. B is 60% more efficient than A, B can do the work alone in ---------- 

Mega finals STD IV mock test

4-Quadratic equation (3)

   
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3-quadratic equations

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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.

Arithmetics --leaking tank

There is a leak in the tank. Because of the leak, the tank which usually is filled in 3 hours, now takes 3.5 hours to be filled. The leak alone will empty the filled tank in ......................... hours.









Answer

Let "x" ltrs/hr be the filling rate of tank.

Under normal situation volume of tank = 3x ltrs

since the tank has a leak, the volume of water fed to tank to make it full is 3.5x  ltrs.

So, excess volume of water lost because of leakage = 3.5x - 3x = 0.5x ltrs

Time taken to loose 0.5x ltrs of water = 3.5 hrs
.
So, time it will take to loose 3x amount of water = (3x/0.5x) x 3.5 = 21 hours

Profit and loss

A man sold 2 cows for Rs 2000 each, neither losing nor gaining in the deal. If he sold one cow at a gain of 29%, at what % loss did he sell the other cow. 

Ans:
Cost Price of 1st Cow = 2000/1.29 = Rs 1550.38
Gain = 2000 - 1550.38 =  449.612
So, loss = 449.612 in the sale of second cow.
So, Cost Price of second cow = 2000+ 449.612 = 2449.612
Loss % = (449.612 / 2449.612) x 100 =18.32%

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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