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Directions: Read the following questions carefully and answer them:
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
_________________________________________________________________

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

___________________________________________________

Traditional Method:

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
___________________________________________________

Traditional Method:

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
________________________________________________

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.