Simplification problems
- 1. In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for?
Options- A. 160
- B. 175
- C. 180
- D. 195 Discuss
Correct Answer: 175
Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
∴ 160 x 2.40 + x x 3.20 = 432
⟹ 3.20x = 432 - 384 = 48
⟹ x = 15.
Hence, total hours of work = (160 + 15) = 175.
- 2. A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
Options- A. 22
- B. 23
- C. 24
- D. 26 Discuss
Correct Answer: 26
Explanation:
Let the number of hens be x and the number of cows be y
Then, x + y = 48 .... (i)
and 2x + 4y = 140 ⟹ x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
∴ The required answer = 26.
- 3. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
Options- A. 10
- B. 35
- C. 62.5
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 62.5
Explanation:
Let the capacity of 1 bucket = x
Then, the capacity of tank = 25x.
| New capacity of bucket = | 2 | x |
| 5 |
| ∴ Required number of buckets = | 25x |
| (2x/5) |
| = | ❨ 25x | x | 5 | ❩ |
| 2x |
| = | 125 |
| 2 |
= 62.5
- 4. The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay?
Options- A. Rs. 1200
- B. Rs. 2400
- C. Rs. 4800
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: Rs. 2400
Explanation:
Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
∴ Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
- 5. A sum of Rs. 1360 has been divided among A, B and C such that A gets ⅔ of what B gets and B gets ¼ of what C gets. B's share is:
Options- A. Rs. 120
- B. Rs. 160
- C. Rs. 240
- D. Rs. 300 Discuss
Correct Answer: Rs. 240
Explanation:
Let C's share = Rs. x
| Then, B's share = Rs. | x | , A's share = Rs. | ❨ | 2 | x | x | ❩ | = Rs. | x |
| 4 | 3 | 4 | 6 |
| ∴ | x | + | x | + x = 1360 |
| 6 | 4 |
| ⟹ | 17x | = 1360 |
| 12 |
| ⟹ x = | 1360 x 12 | = Rs. 960 |
| 17 |
| Hence, B's share = Rs. | ❨ | 960 | ❩ | = Rs. 240. |
| 4 |
- 6. 42060/15 + 5 =?
Options- A. 2804
- B. 2809
- C. 2103
- D. 289 Discuss
Correct Answer: 2809
Explanation:
Given expression = 42060 / 15 + 5
= 2804 +5
=2809.
- 7. 9873 + x = 13200, then x is?
Options- A. 3327
- B. 3237
- C. 3337
- D. None of these Discuss
Correct Answer: 3327
Explanation:
x = 13200 - 9873 = 3327
- 8. (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) =?
Options- A. 1
- B. 1 / 5
- C. 15 / 11
- D. 3 / 11 Discuss
Correct Answer: 15 / 11
Explanation:
Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5)
= (14 + 1) / (10 + 1)
=15 / 11
- 9. [(272 - 32) (124 + 176)] / (17 x 15 - 15) =?
Options- A. 0
- B. 2.25
- C. 300
- D. None of these Discuss
Correct Answer: 300
Explanation:
Given expression = [(272 - 32) (124 + 176)] / (17 x 15 - 15)
= (240 x 300 ) / 240
= 300
- 10. (69 - 14 x 3 + 2) / [ 9 x 5 - (5) 2] =?
Options- A. 1.45
- B. 2.75
- C. 26.5
- D. 265 Discuss
Correct Answer: 1.45
Explanation:
Given expression = (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2]
= (69 - 42 + 2) / (45 - 25)
= 29 / 20
= 1.45
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