Advertisements
Advertisements
Question
If the difference between true discount and banker's discount on a sum due 4 months hence is Rs 20, find true discount, banker's discount and amount of the bill, the rate of simple interest charged being 5% p.a .
Solution
Given the difference B.D - T.D = Rs 20
N = 4 months = `4/12 = 1/3` year
And r = 5% p.a.
Since. B.G = B.D -T.D
∴ B.G = Rs 20.
Let true discount be Rs x
Now, B.G = interest on. T.D for
4 months `(1/3 "year")` at 5 % p.a.
`=> 20 = "x" xx 1/3 xx 5/100`
`=> "x" = (20 xx 100 xx 3)/5 = 1200`
∴ x = Rs 1200
∴ True discount = Rs 1,200
B.G = B.D - T.D
⇒ 20 = B.D - 1,200
∴ BD = Rs. 1,200
Banker's discount is Rs 1,220.
Also, B.D = interest on Face value (F.V) for n years at r% p.a.
Let y be the face value
i.e. B.D = `("y" xx "n" xx "r")/100`
`=> 1220 = ("y" xx 1/3 xx 5)/100`
`=> 1220 xx 100 = "5y"/3`
`=> "y" = (122000 xx 3)/5 = 73200`
∴ y = Rs 73,200
∴ Amount of the bill (face value) is Rs 73,200.
APPEARS IN
RELATED QUESTIONS
An agent charges 12% commission on the sales. What does he earn if the total sale amounts to Rs. 36,000? What does the seller get?
Natarajan and Mr. Gopalan are partners in the company having capitals in the ratio 4 : 5 and the profits received by them are in the ratio 5 :4. If Mr. Gopalan invested capital in the company for 16 months, how long was Mr. Natarajan’s investment in the company?
Ramesh, Vivek, and Sunil started a business by investing capital in the ratio 4 : 5 : 6. After 3 months Vivek withdrew all his capital and after 6 months Sunil withdrew all his capital from the business. At the end of the year, Ramesh received ₹ 6,400 as profit. Find the profit earned by Vivek.
A bill was drawn on 12th April for 3,500 and was discounted on 4th July at 5% p.a. If the banker paid 3,465 for the bill. Find period of the bill.
A manufacturer can sell x items (x > 0) at a price of Rs.(280 - x) each. The cost of producing x items is Rs. (x2 + 40x + 35). Find the number of items to be sold so that the manufacturer can make maximum profit.
If the present worth of a bill due 6 months hence is Rs. 2,500 at 10% per annum, what is the true discount ?
An article is marked at Rs. 1500. A trader allows a discount at 3% and still gains 20% on the cost. Find the cost price of the article.
A wholesaler allows 25% trade discount and 5% cash discount. Find the list price of an article, if it was sold for the net amount of Rs 1,140.
An agent charges 12% commission on the sales. How much does he earn if the total sales amounts to ~ 36,000? How muuch does the seller get from this sale?
Find the Age-Specific Death Rate (SDR) for the following data :
| Age groups (in years) |
Population | Number of deaths |
| 0 - 10 | 11,000 | 220 |
| 10 - 20 | 12,000 | 240 |
| 20 - 60 | 9,000 | 180 |
| 60 and above | 2,000 | 90 |
Find accumulated value after 1 year of annuity immediate in which Rs 20,000 is invested every quarter, at .16% p.a. compounded quarterly.
[Given : (1.04)4 = 1.1699]
The income of an agent remains unchanged though the rate of commission is increased from 5% to 6.25%. Find the percentage reduction in the value of business.
What is the sum due of ₹5,000, due 4 months, hence at 12.5% p.a. simple interest?
Find the true discount, banker's discount and banker's gain on a bill of Rs. 36,600 due 4 months hence at 5% p.a.
A Banker's discount calculated for 1 year is 26 times his gain. Find the rate or interest.
Find tha agents commission at 15% on the first premium if he places insurance for Rs 2,00,000 on the life of a person, the premium being at the rate of Rs 35 per thousand, per annum, paid annually.
