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- Question
The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
Options- A. 3 months
- B. 4 months
- C. 6 months
- D. 8 months
- Correct Answer
- 4 months
ExplanationS.I. on Rs. 1600 = T.D. on Rs. 1680.∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
∴ Time = ❨ 100 x 80 ❩year = 1 year = 4 months. 1600 x 15 3
Banker's Discount problems
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- 1.
The banker's discount on a certain sum due 2 years hence is 11 of the true discount. 10 The rate percent is:
Options- A. 11%
- B. 10%
- C. 5%
- D. 5.5% Discuss
Correct Answer: 5%
Explanation:
Let T.D. be Re. 1.Then, B.D. = Rs. 11 = Rs. 1.10. 10 ∴ Sum = Rs. ❨ 1.10 x 1 ❩ = Rs. ❨ 110 ❩ = Rs. 11. 1.10 - 1 10 ∴ S.I. on Rs. 11 for 2 years is Rs. 1.10
∴ Rate = ❨ 100 x 1.10 ❩% = 5%. 11 x 2 - 2. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options- A.
1 10 - B.
2 5 - C.
2 7 - D.
5 7
Discuss
Correct Answer:2 7
Explanation:
P (getting a prize) = 10 = 10 = 2 . (10 + 25) 35 7 - 3. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options- A.
10 21 - B.
11 21 - C.
2 7 - D.
5 7
Discuss
Correct Answer:10 21
Explanation:
Total number of balls = (2 + 3 + 2) = 7.Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7 = 7C2 ` = (7 x 6) (2 x 1) = 21. Let E = Event of drawing 2 balls, none of which is blue.
∴ n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls. = 5C2 = (5 x 4) (2 x 1) = 10. ∴ P(E) = n(E) = 10 . n(S) 21 - 4. Three unbiased coins are tossed. What is the probability of getting at most two heads?
Options- A. 3/4
- B. 1/4
- C. 3/8
- D. 7/8 Discuss
Correct Answer: 7/8
Explanation:
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
∴ P(E) = n(E) = 7 . n(S) 8 - 5. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Options- A.
1 3 - B.
3 4 - C.
7 19 - D.
8 21 - E.
9 21
Discuss
Correct Answer:1 3
Explanation:
Total number of balls = (8 + 7 + 6) = 21.Let E = event that the ball drawn is neither red nor green = event that the ball drawn is blue. ∴ n(E) = 7.
∴ P(E) = n(E) = 7 = 1 . n(S) 21 3 - 6. The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Options- A. Rs. 400
- B. Rs. 360
- C. Rs. 480
- D. Rs. 320 Discuss
Correct Answer: Rs. 400
Explanation:
T.D. = B.D. x 100 100 + (R x T) = Rs. [ 420 x 100 ] 100 + ❨ 15 x 1 ❩ 3 = Rs. ❨ 420 x 100 ❩ 105 = Rs. 400. - 7. The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:
Options- A. Rs. 36
- B. Rs. 72
- C. Rs. 48
- D. Rs. 96 Discuss
Correct Answer: Rs. 96
Explanation:
T.D. = √P.W. x B.G. = √576 x 16 = 96.- 8. The banker's discount on a sum of money for 1½ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
Options- A. 10%
- B. 13%
- C. 12%
- D. 15% Discuss
Correct Answer: 12%
Explanation:
B.D. for 3⁄2 years = Rs. 558. B.D. for 2 years = Rs. ❨ 558 x 2 x 2 ❩ 3 = Rs. 744 T.D. for 2 years = Rs. 600.
∴ Sum = B.D. x T.D. = Rs. ❨ 744 x 600 ❩ = Rs. 3100. B.D. - T.D 144 Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.
∴ Rate = ❨ 100 x 744 ❩% = 12% 3100 x 2 - 9.
The banker's gain on a certain sum due 1 1 years hence is 3 of the banker's 2 25 discount. The rate percent is:
Options- A.
5 1 % 5 - B.
9 1 % 11 - C.
8 1 % 8 - D.
6 1 % 6
Discuss
Correct Answer:9 1 % 11
Explanation:
Let, B.D = Re. 1.Then, B.G. = Re. 3 . 25 ∴ T.D. = (B.D. - B.G.) = Re. ❨ 1 - 3 ❩ = Re. 22 . 25 25 Sum = ❨ 1 x (22/25) ❩ = Rs. 22 . 1-(22/25) 3 S.I. on Rs. 22 for 1 1 years is Re. 1. 3 2 ∴ Rate = ❨ 100 x 1 ❩% = 100 = 9 1 %. 11 11 22 x 3 3 2 - 10. The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker's gain is:
Options- A. Rs. 20
- B. Rs. 24
- C. Rs. 16
- D. Rs. 12 Discuss
Correct Answer: Rs. 16
Explanation:
B.G. = (T.D.)2 = Rs. ❨ 160 x 160 ❩ = Rs. 16. P.W. 1600
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