11. The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at 75 Km/hr. At what time do they meet?
A. 10 a.m B. 10.30 a.m C. 11 a.m D. 11.30 a.m
Answer: C. 11 a.m
Explanation:
Suppose they meet x hrs after 8 a.m then, [Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 330. Therefore, 60x + 75(x-1) = 330. => x=3. So,they meet at (8+3) i.e, 11a.m.
12. The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?
A. 456 kms B. 482 kms C. 552 kms D. 556 kms
Answer: C. 552 kms
Explanation:
Total distance travelled in 12 hours =(35+37+39+?..upto 12 terms) This is an A.P with first term, a=35, number of terms, n= 12,d=2. Required distance = 12/2[2 x 35+{12-1) x 2] =6(70+23) = 552 kms.
13. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average. Find the speed at which the train must run to reduce the time of journey to 40 minutes.
A. 50 km/hr B. 60 km/hr C. 65 km/hr D. 70 km/hr
Answer: B. 60 km/hr
Explanation:
We are having time and speed given, so first we will calculate the distance. Then we can get new speed for given time and distance. Lets solve it. Time = 50/60 hr = 5/6 hr Speed = 48 mph Distance = S*T = 48 * 5/6 = 40 km New time will be 40 minutes so, Time = 40/60 hr = 2/3 hr Now we know, Speed = Distance/Time New speed = 40*3/2 kmph = 60kmph
14. The least perfect square, which is divisible by each of 21, 36 and 66 is:
A. 213444 B. 214344 C. 214434 D. 231444
Answer: A. 213444
Explanation:
L.C.M. of 21, 36, 66 = 2772. Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11 To make it a perfect square, it must be multiplied by 7 x 11. So, required number = 2?2 x 3?2 x 7?2 x 11?2 = 213444
15. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
A. 57 B. 67 C. 77 D. 87
Answer: C. 77
Explanation:
Money collected = (59.29 x 100) paise = 5929 paise. Number of members = ?5929 = 77.
16. How many two-digit numbers satisfy this property.: The last digit (unit?s digit) of the square of the two-digit number is 8 ?
A. 1 B. 2 C. 3 D. None of these
Answer: D. None of these
Explanation:
A number ending in 8 can never be a perfect square.
17. The square root of 64009 is:
A. 253 B. 347 C. 363 D. 803
Answer: A. 253
Explanation: ?64009=253
18. (17)3.5 x (17)? = 178
A. 2.29 B. 2.75 C. 4.25 D. 4.5
Answer: D. 4.5
Explanation:
Let (17)3.5 x (17)x = 178. Then, (17)3.5 + x = 178. 3.5 + x = 8 x = (8 ? 3.5) x = 4.5
21. If m and n are whole numbers such that m n = 121, the value of (m ? 1) n + 1 is:
A. 1 B. 10 C. 121 D. 1000
Answer: D. 1000
Explanation:
We know that 112 = 121. Putting m = 11 and n = 2, we get: (m ? 1) n + 1 = (11 ? 1) (2 + 1) = 103 = 1000.
22. If 3(x ? y) = 27 and 3(x + y) = 243, then x is equal to:
A. 0 B. 2 C. 4 D. 6
Answer: C. 4
Explanation: 3x ? y = 27 = 33 x ? y = 3 ?.(i) 3x + y = 243 = 35 x + y = 5 ?.(ii) On solving (i) and (ii), we get x = 4.
23. Rajender invests a part of Rs. 12000 in 12% stocks at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
A. Rs. 4500 B. Rs. 6000 C. Rs. 5500 D. Rs 4000
Answer: D. Rs 4000
Explanation:
Let investment in 12% stock is Rs. x. Investment in 15% stock Rs. (12000 ? x). (12/120) * x + 15/125(12000-x) = 1360 5x + 72000 -6x hence x = 4000
24. A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is?
A. 8% B. 9.7% C. 7.5% D. None of these
Answer: A. 8%
Explanation:
By investing Rs. 1552, income = Rs. 128. By investing Rs. 97, income = Rs. (128/1552) * 97= Rs. Dividend = 8%.
25. By investing Rs. 1620 in 8% stock, Sandeep earns Rs. 135. The stock is then quoted at?
A. Rs. 106 B. Rs. 80 C. Rs. 96 D. Rs. 108
Answer: C. Rs. 96
Explanation:
To earn Rs. 135, investment = Rs. 1620. To earn Rs. 8, investment = Rs. (1620/135) * 8= Rs.96. Market value of Rs. 100 stock = Rs. 96.
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