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- Question
There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options- A. 20
- B. 80
- C. 100
- D. 200
- Correct Answer
- 100
Explanation
Let the number of students in rooms A and B be x and y respectively.Then, x - 10 = y + 10 ⟹ x - y = 20 .... (i)
and x + 20 = 2(y - 20) ⟹ x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
∴ The required answer A = 100.
- 1. A man has Rs.480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
Options- A. 45
- B. 60
- C. 75
- D. 90 Discuss
- 2.
(469 + 174)2 - (469 - 174)2 =? (469 x 174)
Options- A. 2
- B. 4
- C. 295
- D. 643 Discuss
- 3. The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:
Options- A. 279
- B. 283
- C. 308
- D. 318 Discuss
- 4. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
Options- A. 123
- B. 127
- C. 235
- D. 305 Discuss
- 5. The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options- A. 276
- B. 299
- C. 322
- D. 345 Discuss
- 6. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?
Options- A. 19
- B. 28
- C. 30
- D. 37 Discuss
- 7. A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
Options- A. 30 birds
- B. 60 birds
- C. 72 birds
- D. 90 birds Discuss
- 8. One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund?
Options- A. Rs. 30,000
- B. Rs. 50,000
- C. Rs. 60,000
- D. Rs. 90,000 Discuss
- 9. If a - b = 3 and a2 + b2 = 29, find the value of ab.
Options- A. 10
- B. 12
- C. 15
- D. 18 Discuss
- 10. The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
Options- A. Rs. 3500
- B. Rs. 3750
- C. Rs. 3840
- D. Rs. 3900 Discuss
Simplification problems
Search Results
Correct Answer: 90
Explanation:
Let number of notes of each denomination be x
Then x + 5x + 10x = 480
⟹ 16x = 480
∴ x = 30.
Hence, total number of notes = 3x = 90.
Correct Answer: 4
Explanation:
| Given exp. = | (a + b)2 - (a - b)2 |
| ab |
| = | 4ab |
| ab |
= 4 (where a = 469, b = 174.)
Correct Answer: 308
Explanation:
| Other number = | ❨ | 11 x 7700 | ❩ | = 308. |
| 275 |
Correct Answer: 127
Explanation:
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.
Correct Answer: 322
Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14).
∴ Larger number = (23 x 14) = 322.
Correct Answer: 30
Explanation:
Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 - 63x ⟺ 120x = 40
| x = | 1 |
| 3 |
| Number of floors covered by David in (1/3) min. = | ❨ | 1 | x 57 | ❩ | = 19. |
| 3 |
So, their paths cross at (11 +19) i.e., 30th floor.
Correct Answer: 30 birds
Explanation:
Let the total number of shots be x . Then,
| Shots fired by A = | 5 | x |
| 8 |
| Shots fired by B = | 3 | x |
| 8 |
| Killing shots by A = | 1 | of | 5 | x | = | 5 | x |
| 3 | 8 | 24 |
| Shots missed by B = | 1 | of | 3 | x | = | 3 | x |
| 2 | 8 | 16 |
| ∴ | 3x | = 27 or x = | ❨ | 27 x 16 | ❩ | = 144. |
| 16 | 3 |
| Birds killed by A = | 5x | = | ❨ | 5 | x 144 | ❩ | = 30. |
| 24 | 24 |
Correct Answer: Rs. 60,000
Explanation:
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x ) respectively. Then,
| 1 | x = | 1 | (150000 - x) |
| 3 | 2 |
| ⟹ | x | + | x | = 75000 |
| 3 | 2 |
| ⟹ | 5x | = 75000 |
| 6 |
| ⟹ x = | 75000 x 6 | = 90000 |
| 5 |
∴ Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
Correct Answer: 10
Explanation:
2 ab = ( a 2 + b 2 ) - ( a - b ) 2
= 29 - 9 = 20
⟹ab = 10.
Correct Answer: Rs. 3900
Explanation:
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
| Then, 10x = 4y or y = | 5 | x. |
| 2 |
∴ 15x + 2y = 4000
| ⟹ 15x + 2 x | 5 | x = 4000 |
| 2 |
⟹ 20x = 4000
∴ x = 200.
| So, y = | ❨ | 5 | x 200 | ❩ | = 500. |
| 2 |
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
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