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- Question
- In a two digit positive number the unit digit is equal to the square of ten's place digit. The difference between the original number and the number formed by interchanging the digit is 54. What of 40% of the original number?
Options- A. 64
- B. 73
- C. 84
- D. Couldn't be determined
- Correct Answer
-
ExplanationLet ten's place digit be a and unit's place digit be a2
Original number = 10 x a + 1 x a2 = 10a + a2
The number formed by interchanging the digits,
New number = 10 x a 2 + 1 x a = 10a 2 + a
According to the question
(10a2 + a) - ( 10a + a2) = 54
? 10a2 + a - 10a - a 2 = 54
? 9a2 - 9a = 54
? 9( a2 - a) = 54
? ( a2 - a) = 54/9
? ( a2 - a) = 6
? a2 - a - 6 = 0
? a2 - 3a + 2a - 6 = 0
? a (a - 3) + 2 (a - 3) = 0
? (a - 3) (a + 2) = 0
? a = 3, - 2
? Ten,s digit = a = 3
Unit's digit = a2 = 32 = 9
Original number = 39
? Required number = 39 x 40/100 = 15.6 - 1. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Options- A. 400 kg
- B. 560 kg
- C. 600 kg
- D. 640 kg Discuss
- 2. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
Options- A. 36
- B. 45
- C. 48
- D. 49 Discuss
- 3. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Options- A. 230 m
- B. 240 m
- C. 260 m
- D. 270 m Discuss
- 4. A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
Options- A. Rs. 456
- B. Rs. 458
- C. Rs. 558
- D. Rs. 568 Discuss
- 5. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options- A. Rs. 1900
- B. Rs. 2660
- C. Rs. 2800
- D. Rs. 2840 Discuss
- 6. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
Options- A. Rs. 400
- B. Rs. 500
- C. Rs. 600
- D. Rs. 800 Discuss
- 7. If log10 2 = 0.3010, then log2 10 is equal to:
Options- A.
699 301 - B.
1000 301 - C. 0.3010
- D. 0.6990 Discuss
- 8. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Options- A. 30 days
- B. 40 days
- C. 60 days
- D. 70 days Discuss
- 9. A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options- A. 4 months
- B. 5 months
- C. 6 months
- D. 8 months Discuss
- 10. A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be
Options- A. 1, 2
- B. 2, 3
- C. 3, 2
- D. 4, 1 Discuss
More questions
Correct Answer: 600 kg
Explanation:
| Profit on 1st part Profit on 2nd part | ||
| 8% | Mean Profit 14% |
18% |
| 4 | 6 | |
Ration of 1st and 2nd parts = 4 : 6 = 2 : 3
| ∴ Quantity of 2nd kind = | ❨ | 3 | x 1000 | ❩kg | = 600 kg. |
| 5 |
Correct Answer: 48
Explanation:
Relative speed = (60+ 90) km/hr
| = | ❨ | 150 x | 5 | ❩m/sec |
| 18 |
| = | ❨ | 125 | ❩m/sec. |
| 3 |
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
| Required time = | ❨ | 2000 x | 3 | ❩sec = 48 sec. |
| 125 |
Correct Answer: 270 m
Explanation:
| Speed = | ❨ | 72 x | 5 | ❩m/sec | = 20 m/sec. |
| 18 |
Time = 26 sec.
Let the length of the train be x metres.
| Then, | x + 250 | = 20 |
| 26 |
⟹ x + 250 = 520
⟹ x = 270.
Correct Answer: Rs. 558
Explanation:
| Area to be plastered | = [2(l + b) x h] + (l x b) |
| = {[2(25 + 12) x 6] + (25 x 12)} m2 | |
| = (444 + 300) m2 | |
| = 744 m2. |
| ∴ Cost of plastering = Rs. | ❨ | 744 x | 75 | ❩ | = Rs. 558. |
| 100 |
Correct Answer: Rs. 2660
Explanation:
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
| ∴ B's share = Rs. | ❨ | 7030 x | 14 | ❩ | = Rs. 2660. |
| 37 |
Correct Answer: Rs. 500
Explanation:
| Then, | [ | P | ❨ | 1 + | 10 | ❩ | 2 | - P | ] | = 525 |
| 100 |
| ⟹ | P | [ | ❨ | 11 | ❩ | 2 | - 1 | ] | = 525 |
| 10 |
| ⟹ P = | ❨ | 525 x 100 | ❩ | = 2500. |
| 21 |
∴ Sum = Rs . 2500.
| So, S.I. = Rs. | ❨ | 2500 x 5 x 4 | ❩ | = Rs. 500 |
| 100 |
Correct Answer:
| 1000 |
| 301 |
Explanation:
| log2 10 = | 1 | = | 1 | = | 10000 | = | 1000 | . |
| log10 2 | 0.3010 | 3010 | 301 |
Correct Answer: 60 days
Explanation:
| Then, x + y = | 1 | and 16x + 44y = 1. |
| 30 |
| Solving these two equations, we get: x = | 1 | and y = | 1 |
| 60 | 60 |
| ∴ B's 1 day's work = | 1 | . |
| 60 |
Hence, B alone shall finish the whole work in 60 days.
Correct Answer: 8 months
Explanation:
| Then, | ❨ | 85000 x 12 | = | 3 | ❩ |
| 42500 x x | 1 |
| ⟹ x = | ❨ | 85000 x 12 | ❩ | = 8. |
| 42500 x 3 |
So, B joined for 8 months.
Correct Answer: 2, 3
Explanation:
4 | x y = (5 x 1 + 4) = 9 -------- 5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37 -------- | 1 -4 Now, 37 when divided successively by 5 and 4, we get 5 | 37 --------- 4 | 7 - 2 --------- | 1 - 3 Respective remainders are 2 and 3.
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