Solution: (e)
Let the cost price of the articles be ₹100
Marked Price = ₹130
After giving a discount of 10% the selling price of the
articles = 0.9 × 130 = 117
So, actual profit percent = \(\displaystyle \frac{{117-100}}{{100}}\times 100=17\%\)

Solution: (a)
Let original price of TV = x
Customer paid = 111% of x = ₹ 133200
x = \(\displaystyle \frac{{133200\times 100}}{{111}}=120000\)

Solution: (c)
Let cost price of article = x
Now 55% of x = Rs. 4510
Therefore x = \(\displaystyle \frac{{4510}}{{55}}\times 100=8200\)
To gain profit of 45% selling price is 145 % of 8200 is ₹11890

Solution: (a)
Cost of 23 bracelet purchased at rate of ₹ 160/bracelet
= ₹ 23 × 160 = ₹ 3680
If profit earned is 15%, then
Profit amount = \(\displaystyle \frac{{3680\times 15}}{{100}}=552\)
Total amount Meera have after selling 23 bracelets
= 3680 + 552 = 4232
S.P. of one bracelet = \(\displaystyle \frac{{4232}}{{23}}=184\)

Solution: (d)
Let x be the price of one capsule y be the total number of capsule.
xy = 216 …(1)
(x – 10) (y + 15) = 216 …(2)
From eqs (1) and (2)
\(\displaystyle \begin{array}{l}\left( {\frac{{216}}{y}-10} \right)(y+15)=216\\(216-10y)(y+15)=216y\\216y+216\times 15-10{{y}^{2}}-150y=216y\\216y+3240-10{{y}^{2}}-150y=216y\\-10{{y}^{2}}-150y+3240=0\\{{y}^{2}}+15y-324=0\\y=12\end{array}\)

Solution : (a)

SP of the mixture = ₹ 15

Therefore, CP of the mixture = \(\displaystyle 15\times \frac{{100}}{{125}}=12\)

Now, by the rule of mixture,

\(\displaystyle \Rightarrow \)Ratio of milk and water in the mixture

= 12 : 4 = 3 : 1

Alternate method

We know:

Profit = Selling Price – Cost Price

Let’s assume that the cost price of the mixture is x.

Profit = Selling Price – Cost Price

0.25x = 15 – x

0.25x + x = 15

x = 15/1.25

x = 12

So, the cost price of the mixture is Rs. 12 per litre.

We know that the cost price of pure milk is Rs. 16 per litre.

Let’s assume that the ratio of milk to water in the mixture is a:b.

Cost Price = \(\displaystyle \left( {\frac{a}{{a+b}}} \right)\times 16+\left( {\frac{b}{{a+b}}} \right)\times 0\)

\(\displaystyle 12=\left( {\frac{a}{{a+b}}} \right)\times 16\)

\(\displaystyle \frac{a}{{a+b}}=\frac{3}{4}\)

This means that for every 4 parts of the mixture, 3 parts are pure milk, and 1 part is water. So, the respective ratio of milk to water in the mixture is 3:1

One more method

Let X is the cost of pure Milk. Then,

Cost of Mixture,

X + 25% of X = 15

100X + 25X = 15 × 100

125X = 15 × 100

X = 1500/125 = Rs. 12.

So, Milk of Rs. 12 sold at Rs. 15.

Part of Milk buyer gets in 12,

In Rs. 16 = 1 lit milk.

So, in 12 = \(\displaystyle \frac{{12}}{{16}}=\frac{3}{4}\)  part milk he gets and \(\displaystyle \frac{1}{3}\) part water.

Therefore ratio Milk : water

\(\displaystyle \frac{3}{4}:\frac{1}{3}\)  = 3 : 1

Solution: (b)
S.P. for the first car = ₹ 5,400 and profit = 20%
We know,
CP= \(\displaystyle \frac{{100}}{{100+profit\%}}\times SP\)
\(\displaystyle \Rightarrow \)C.P. for the first car = \(\displaystyle \frac{{100}}{{120}}\times 5400=4500\)
Similarly,
S.P. for the second car = ₹ 3,300 and profit = 10%
\(\displaystyle \Rightarrow \)C.P. for second car = \(\displaystyle \frac{{100}}{{110}}\times 3300=3000\)
and loss = \(\displaystyle \frac{{75}}{8}\%\)
S.P. of three cars = 5,400 + 3,300 + 4350 = ₹ 13,050
\(\displaystyle \Rightarrow \)Total C.P. for the three cars = \(\displaystyle \frac{{100\times 8}}{{725}}\times 13050\)
= 14,400
Therefore, C.P. for third car = 14,400 – 4,500 – 3,000 = ₹ 6,900

Solution: (c)

Let the second discount be x%. Then(100 – x)% of 90% of 720 = 550.80

\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{100-x}}{{100}}\times \frac{{90}}{{100}}\times 720=\frac{{55080}}{{100}}\)

\(\displaystyle \Rightarrow \)\(\displaystyle 100-x=\frac{{55080\times 100}}{{90\times 720}}=85\)

\(\displaystyle \Rightarrow \) x=100 – 85 = 15%

Alternate method

MP of a watch is Rs.720

SP of a watch is Rs.550.80

We know that,

Equivalent discount = a + b – (ab/100)

where, a is the first discount. b is the second discount.

% Discount = (MP – SP)/MP × 100

⇒ % discount = (720 – 550.80)/720 × 100

⇒ % discount = 169.2/72 × 10

⇒ % discount = 23.5

Equivalent discount = a + b – (ab/100)

⇒ 23.5 = 10 + b – (10 × b/100)

⇒ 13.5 = b – 0.1b

 ⇒ 13.5 = 0.9b

⇒ b = 13.5/0.9

⇒ b = 15

The rate of the second discount is 15%.

One more method

Marked price = Rs. 720
Discount = 10%

\(\displaystyle \Rightarrow \) After a discount of 10%,

SP= Rs \(\displaystyle \left( {\frac{{720\times 90}}{{100}}} \right)\) = Rs. 648
Final S.P. = Rs. 550.80

\(\displaystyle \Rightarrow \)Discount = Rs. (648 – 550.80) = Rs. 97.20
If the second discount be \(\displaystyle x\) %, then

\(\displaystyle {\frac{{648\times x}}{{100}}}\) = 97.20

\(\displaystyle {\Rightarrow x=\frac{{97.2\times 100}}{{648}}}\)= 15%

Solution: (b)
Let the C.P. of horse = ₹ x
Then the C.P. of carriage = ₹ (3000 – x)
20% of x – 10% of (3000 – x) = 2% of 3000
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{5}-\frac{{(3000-x)}}{{10}}=60\)
\(\displaystyle \Rightarrow \)2x – 3000 + x = 600
\(\displaystyle \Rightarrow \) 3x = 3600
\(\displaystyle \Rightarrow \) x=₹ 1200

Solution: (c)
Let the cost price of manufactures is = P
Selling price of manufacturer = \(\displaystyle p+p\times \frac{{18}}{{100}}=\frac{{59p}}{{50}}\)
Wholesaler selling price = \(\displaystyle \frac{{354p}}{{250}}+\frac{{354p}}{{250}}\times \frac{{20}}{{100}}\)
= \(\displaystyle \frac{{59p}}{{50}}+\frac{{59p}}{{250}}=\frac{{354p}}{{250}}\)
Retailer selling price = \(\displaystyle \frac{{354p}}{{250}}+\frac{{354p}}{{250}}\times \frac{{25}}{{100}}\)
= \(\displaystyle \frac{{354p}}{{240}}+\frac{{177p}}{{500}}=\frac{{805p}}{{500}}\)
Now, \(\displaystyle \frac{{805p}}{{500}}=30.09\)
\(\displaystyle \Rightarrow \) P=17

Shortcut
P= \(\displaystyle (\frac{{100}}{{118}}\times \frac{{100}}{{120}}\times \frac{{100}}{{120}}\times 30.09)=17\)