Important for :
1
Sanjay purchased a hotel worth rupees 10 lakhs and Anita purchased a car worth Rs. 16 lakh. The value of hotel every year increase by 20% of the previous value and the value of car every depreciates by 25%. What is the difference between the price of hotel and car after 3 years?
» Explain it
A
Amount of the hotel after 3 years =10 lakh
 ( 1 + 20 ) 100
3 .

= 10 lakh
 ( 6 ) 5
3   = 10,00,000 ×  216
125

⇒ 1728000.

Amount of the car after 3 years =16 lakh
 ( 1 - 25 ) 100
3 .

= 16 lakh
 ( 3 ) 4
3

 = 16,00,000 × 27 64

= 6,75,000.

Difference = 17,28,000 - 6,75,000  = 10,53,000.

Hence, option A is correct.

2
C.I. Rs. 5000 for 3 years at 8% for 1st year and 10% for 2nd year and 12% for 3rd year will be-
» Explain it
B
Rate of interest for 1st, 2nd and 3rd year = 8%, 10% and 12%

Now, P = 5000, T = 3 years

By the net% effect we would calculate the effective compound rate of interest for 3 years = 33.056% (Refer to sub-details)

Therefore, CI = 33.056% of 5000

 CI = 33.056 × 5000 = ₹ 1652.8 100
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Sub-details:

Calculation of effective compound rate of interest for 3 years will be as follows.

For the first 2 years, let's apply the net% effect.

Here, x = 8 and y = 10%

 Net% effect = x + y = xy 100

 = 8 + 10 + 8 × 10 = 18 + 0.8 = 18.8% 100

Now let's take this 18.8% as x and 12% as y for the calculation of 3rd year.

 = 18.8 + 12 + 18.8 × 12 = 30.8 + 2.256 = 33.056% 100

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C.I. = 5000
 ( 1 + 8 ) 100
 ( 1 + 10 ) 100
 ( 1 + 12 ) 100
– 5000.

= 5000
 [( 27 ) 25
 ( 11 ) 10
 ( 28 ) 25
– 1 ]

 =5000 [ 27 × 11 × 28 – 1 ] = 5000 [ 27 × 11 × 28 – 6250 ] . 6250 6250

 = 4 × 2066 5

= Rs. 1652.8.

Hence, option B is correct.

3
A has lent some money to B at 6% p.a. and C at 10% at the end of the year he has gain the over all interest at 8% p.a. in what ratio has he lent the money to A and B?
» Explain it
C
By alligation and mixture:

 6 10 ↘ ↙ 8 ↙ ↘ 2 2

the ratio is- 2 : 2 = 1:1.

Hence, option C is correct.

4
Loan of 10,000 was lent to a person at for 3 years @ 10% for 1st year, 15% for rest  2 years. Find the amount?
» Explain it
B
Rate of interest for 1st, 2nd and 3rd year = 10%, 15% and 15%

P = 10000, T = 3 years,

By the net% effect we would calculate the effective compound rate of interest for 3 years = 45.475% (Refer to sub-details)

Principal = 100%; Amount (P + CI) = 100 + 45.475 = 145.475%

100%  ≡  ₹ 10000
145.475%  ≡  ₹ x

By the cross multiplication, we get

 x = 10000 × 145.475 = ₹ 14547.5 100
_________________________________________________________________

Sub-details:

Calculation of effective compound rate of interest for 3 years will be as follows.

For the first 2 years, let's apply the net% effect.

Here, x = 10 and y = 15%

 Net% effect = x + y = xy 100

 = 10 + 15 + 10 × 15 = 25 + 1.5 = 26.5% 100

Now let's take this 26.5% as x and 15% as y for the calculation of 3rd year.

 = 26.5 + 15 + 26.5 × 15 = 41.5 + 3.975 = 45.475% 100
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 A = 10,000 ( 1 + 10 )( 1 + 15 ) 2 100 100

 A = 10,000 ( 11 )( 20 + 3 ) 2 10 20

 A = 10,000 ( 11 )( 23 )( 23 ) . 10 20 20

 ⇒ 10 × 11 × 23 × 23 ⇒ Rs. 14547.5. 4

Hence, option B is correct.

5
The difference between C.I. and S.I. on a sum of money lent for 2 years at 10% is Rs. 40. The sum is:
» Explain it
D
Method I:

To solve this question, we can apply a short trick approach

 Sum = Difference × 1002 r2

Given,

Difference = 40,  r = 10%

By the short trick approach, we get

 Sum = 40 × 1002 = 4000/- 102
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Method II:

We can solve it by the net% formula,

Rate % of SI for 2 yr at 10% pa = 10 × 2 = 20%

Rate % of CI for 2 yr at 10%,

 = 10 + 10 + 10 × 10 = 21% 100

% rate difference of CI and SI = 21% – 20 = 1%

Let the sum be x, then

1% of x = 40

 x = 40 × 100 = ₹ 4,000 1

Hence, option D is correct.