## Discount

#### Discount

1. Two successive discounts of 20% and 5% are equivalent to a single discount of
1. 25%
2. 24%
3. 18%
4. 15%

1. Here, r1 = 20% and r2 = 5%
∴ Required percentage
= r1 + r2 - (r1 x r2)/100%

##### Correct Option: B

Here, r1 = 20% and r2 = 5%
∴ Required percentage
= r1 + r2 - (r1 x r2)/100%
= 20 + 5 - (20 x 5)/100
= 25 - 1
=24%

1. The present worth of ₹ 920 due at the end of 3 years at 5 % simple interest per annum is :
1. ₹780
2. ₹850
3. ₹800
4. ₹810
5. None of these

1. Given :- Amount = ₹ 920 , Rate = 5% and Time = 3 years

 Present Worth = Amount × 100 100 + ( Rate × Time )

##### Correct Option: C

Given :- Amount = ₹ 920 , Rate = 5% and Time = 3 years

 Present Worth = Amount × 100 = ₹ 920 × 100 = ₹ 920 × 100 = ₹ 800 100 + ( Rate × Time ) 100 + ( 3 × 5 ) 115

1. If the simple interest on a certain sum is due for some years at 6 % is ₹180, and the discount at 5 % on the same amount is ₹140. Find the sum and the time.
1.  ₹ 2100 and 1 3 Year 7
2.  ₹ 2200 and 2 3 Year 7
3.  ₹ 2000 and 2 3 Year 7
4.  ₹ 2300 and 1 3 Year 7
5. None of these

1. Given :- Simple Interest = ₹180 , Rate = 6%

 Banker 's Discount or Simple Interest at 5% = 180 × 5 = ₹ 150 6

Banker 's Discount = ₹ 150
True Discount at 5% = ₹140.
 Sum Due = Banker 's Discount × True Discount = 150 × 140 = ₹ 2100 Banker 's Discount - True Discount 150 - 140
 ∴ Time = Interest × 100 years Sum due × Rate

##### Correct Option: A

Given :- Simple Interest = ₹180 , Rate = 6%

 Banker 's Discount or Simple Interest at 5% = 180 × 5 = ₹ 150 6

Banker 's Discount = ₹ 150
True Discount at 5% = ₹140.
 Sum Due = Banker 's Discount × True Discount = 150 × 140 = ₹ 2100 Banker 's Discount - True Discount 150 - 140
 ∴ Time = Interest × 100 years Sum due × Rate

 Time = 180 × 100 = 1 3 Year 2100 × 6 7

1. The banker’s gain on a certain sum of money is due for 9 months at 4 % p.a. is ₹2.25. The sum is :
1. ₹2575
2. ₹2500
3. ₹2250
4. ₹3250
5. None of these

1.  Here , Banker 's Gain = ₹2.25 , Time = 9 months = 9 = 3 years 12 4

Banker 's Gain is the interest on True Discount .
 True discunt = Banker 's Gain × 100 Rate × Time
 ∴ True Discount ( T.D. ) = 2.25 × 100 = ₹ 75 3/4 × 4

Banker 's Discount ( B.D. ) = True Discount ( T.D. ) + Banker 's Gain ( B.G. )
B.D.= ₹75 + ₹2.25 = ₹77.25
 ∴ Sum due = B.D. × T.D. B.G.

##### Correct Option: A

 Here , Banker 's Gain = ₹2.25 , Time = 9 months = 9 = 3 years 12 4

Banker 's Gain is the interest on True Discount .
 True discunt = Banker 's Gain × 100 Rate × Time
 ∴ True Discount ( T.D. ) = 2.25 × 100 = ₹ 75 3/4 × 4

Banker 's Discount ( B.D. ) = True Discount ( T.D. ) + Banker 's Gain ( B.G. )
B.D.= ₹75 + ₹2.25 = ₹77.25
 ∴ Sum due = B.D. × T.D. = ₹ 77.25 × 75 B.G. 2.25

Sum due = ₹ 2575.

1. The present worth of a bill of ₹1764 due for 2 years at 5 % compound interest is :
1. ₹1650
2. ₹1700
3. ₹1600
4. ₹1714
5. None of these

1. Given that :- Amount = ₹1764 , Rate = 5% and Time = 2 years

 ∴ Present Worth ( P.W. ) = Amount ÷ 1 + Rate Time 100

##### Correct Option: C

Given that :- Amount = ₹1764 , Rate = 5% and Time = 2 years

 ∴ Present Worth ( P.W. ) = Amount ÷ 1 + Rate Time 100

 P.W. = ₹1764 ÷ 1 + 5 × 1 + 5 100 100
 = ₹1764 × 440 = ₹1600 441