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प्रश्न
Find the true discount Banker’s discount and Banker’s gain on a bill of ₹ 4,240 due 6 months hence at 9% p.a.
उत्तर
Given, S.D. = ₹ 4,240
n = `6/12 = 1/2` year, r = 9% p.a.
Since, B.D. = `("S.D." xx "n" xx "r")/100`
∴ B.D. = `(4,240 xx 1/2 xx 9)/100`
= `(4,20 xx 9)/(100 xx 2)`
∴ B.D. = ₹ 190.80
Let true discount be ₹ x
Now, B.D. = T.D. + Interest on T.D. for `1/2` year at 9% p.a.
∴ 190.80 = `x + (x xx 1/2 xx 9/100)`
∴ 190.80 = `x + (9x)/200`
∴ 190.80 = `(209x)/200`
∴ x = `(190.80 xx 200)/209`
∴ x = ₹ 182.58
∴ T.D. = ₹ 182.58
Also, B.G. = B.D. – T.D. = 190.8 – 182.58
∴ B.G. = ₹ 8.22
∴ True discount, banker’s discount and banker’s gain are ₹ 182.58, ₹ 190.80 and ₹ 8.22 respectively.
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संबंधित प्रश्न
Find the true discount, banker’s discount and banker’s gain on a bill of ₹ 4,240 due 6 months hence at 9% p.a.
A bill drawn on 5th June for 6 months was discounted at the rate of 5% p.a. on 19th October. If the cash value of the bill is ₹ 43,500, find face value of the bill.
If difference between true discount and banker’s discount on a sum due 4 months hence is ₹ 20. Find true discount, banker’s discount and amount of bill, the rate of simple interest charged being 5%p.a.
A bill of a certain sum drawn on 28th February 2007 for 8 months was encashed on 26th March 2007 for ₹ 10,992 at 14% p.a. Find the face value of the bill.
Banker’s gain is simple interest on ______.
When only one discount is given, then ______
The difference between face value and present worth is called ______.
Fill in the Blank.
The banker’s discount is also called _______.
The difference between the banker’s discount and true discount is called sum due.
A merchant buys some mixers at 15% discount on catalogue price. The catalogue price is ₹ 5,500 per piece of a mixer. The freight charges amount to `2 1/2` % on the catalogue price. The merchant sells each mixer at 5% discount on catalogue price. His net profit is ₹ 41,250. Find a number of mixers.
A bill was drawn on 14th April 2005 for ₹ 3,500 and was discounted on 6th July 2005 at 5% per annum. The banker paid ₹ 3,465 for the bill. Find the period of the bill.
Choose the correct alternative:
The marked price is also called as ______
The difference between the ______ and the true discount is called Banker’s Gain (B.G). It is equal to the interest on true discount
State whether the following statement is True or False:
A person can get both, trade discount and cash discount
State whether the following statement is True or False:
The sum due is also called as Cash value
A bill of ₹ 8,000 drawn on 5th January 2019 for 8 months was discounted for ₹ 7,680 on a certain date. Find the date on which it was discounted at 10% p.a.
Solution: Banker’s Discount
B.D.= F.V. − C.V. = 8,000 −7,680 = ₹ 320
Date of drawing = 5th January 2019
Period = 8 months
Nominal due date = `square`
Legal due date = `square`
B.D. = Interest on F.V. for n at 10% p.a.
∴ B.D. = `("F.V." xx "n"/365 xx "r")/100`
∴ 320 = `(8000 xx "n"/365 xx 10)/100`
∴ n = `square` days
| April | May | June | July | Aug | Sep | Total |
| 15 | 31 | 30 | 31 | 31 | `square` | `square` |
∴ Date of discounting is `square`
The difference between true discount and banker's discount on a bill due 6 months hence at 4% is ₹ 160. Calculate true discount, banker's discount and amount of bill.
The banker’s discount is also called true discount.
