A wall clock gains 2 minutes in 12 hours, while a table clock loses 2 minutes every 36 hours. Both are set right at 12 noon on Tuesday. The correct time when both show the same time next would be
12.30 at night, after 130 days
12 noon, after 135 days
12 midnight, after 135 days
B.
12 noon, after 135 days
A wall clock gains 2 min in every 12 hours, so it would gain 6 min in 36 hours.
and table clock losses two minutes in every 36 hours.
So, in every 36 hours they difference between them is 8 min.
They will be at the same time when the difference between them is 12 hours.
Hence, 8 min = 36 hours
So, 1 min difference =
Or 12 x 60 min difference in
or 3240 hours is 135 days.
Hence both clocks will show same time at 12 noon after 135 days.
There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively. In 36 minutes, how many times will the bells ring simultaneously?
13
12
6
5
A.
13
L.C.M. of 3, 6, 9, 12 and 15 = 180 seconds
∴ Bells will ring together after every 180 seconds
∴ Required answer
Insert the missing number
3, 18, 12, 72, 66, 396 ?
300
380
350
390
D.
390
3 x 6 = 18
18 - 6 = 12
12 x 6 = 72
72 - 6 = 66
66 x 6 = 396
396 - 6 = 390
In four consecutive prime numbers that are in ascending order, the product of the first three is 385 and that of the last three is 1001. The largest given prime number is
11
13
17
19
B.
13
Let the four consecutive prime numbers be a, b, c and d where a < b < c < d.
∴ abc = 385 and bcd = 1001
∴ HCF = bc
(H.C.F. of 385 and 1001 is 77)
∴ bc = 77
∵ bcd = 1001
A and B started a business by investing ₹ 3,50,000 and ₹ 1,40,000 respectively. A gets 20% of the yearly profit for managing the business. Thereafter the profit is divided in the ratio of the capital. If A receives totally ₹ 38,000 more than B at the end of a year, then the profit is
₹ 28,000
₹ 2,80,000
₹ 1,05,000
₹ 70,000
D.
₹ 70,000
Let the total profit be Rs. x
Now, A gets 20% profit for managing business =
Remaining profit =
Thereafter, remaining profit will be distributed in the profit sharing ratio.
i.e. (350000 : 140000) = 5 : 2
∴ A's total share =
∴ Difference
(i) - (ii) = 38000
If a^{3}b = abc = 180, a, b, c are positive integers, then the value of c is
110
1
4
25
B.
1
a^{3}b = abc = 180
⟹ a^{2}b = bc, ⟹ a^{2 }= c
n is a whole number which when divided by 4 gives the remainder 3. The remainder when 2n is divided by 4 is
1
2
3
0
B.
2
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