V = 10U .
Then U is less than V by 9 times.
U is less than V by [ (9/10) × 100 ]% = 90%.
Whole work is done by A in (3 x 4) = 12 days.
Whole work is done by B in (4 x 6) = 24 days.
A’s wages : B’s wages = A’s 1 day’s work : B’s 1 day’s work = 1/12 : 1/24 = 2 : 1
A’s share = Rs. 2/3 * 210 = Rs. 140.
A gives B 30 points, which means A gets 90 points i.e, (120 - 90)
Similarly A gives C 40 points, which means A gets 80 points i.e,(120 - 40)
A/B = 90/120 A/C = 80/120
B/A * A/C = 120/90 * 80/120 = 80/90
So, 10 points out of 90 can be given.
A/B = 7/4
Ratio of the speeds of A and B = 7/4.
We know speed is proportional to distance
Thus, in race of 7 m, A gains 3 m over B.
3 m are gained by A in a race of 7 m.
90 m will be gained by A in race of = 7/3* 90 =210
Thus, winning post is 210 m away from the starting point.
Let A’s 1 day’s work = X and B’s 1 day’s work = Y.
Then, X + Y = 1/7 and 3X + 1/3Y = 1/3
Solving we get, X = 3/28 and Y = 5/28
A’s one day’s work = 3/28
So, A alone could complete the work in = 28/3 = 9 1/3 days.
B / (A + B) = 40/100 = 2/5
(A + B)/B - 1 = 5/2 – 1
A/B in % = 3/5 * 100 = 150%.
Alternate method.
B = 0.4(A + B) (Since B is 40% of A + B)
B = 0.4A + 0.4B
0.6B = 0.4A
A = (0.6/0.4)B
A = 1.5 B which means A is 150% of B.
$\log_{5}{1728}$ = log 1728/log 5
= (log 64 x 27) / log 5 = ( log 64 + log 27)/log 5 = (log 26 + log 33) / log 5
log 5 = log(10/2) = log 10 - log 2
= (6log2 + 3log3) /(log 10 - log 2) (we convert everything in the form of log 2 and log 3)
= [ (6 x 0.3010) + (3 x 0.4771) ] / (1 - 0.3010)
= 3.2373/0.699
= 4.631.
Cost Price = 0.8x (20% less)
Selling Price = 1.2x (20% more)
Gain % = [(SP - CP) / CP] x 100% = (1.2x - 0.8x)/0.8x
= 0.4x / 0.8x = 1/2
= 50% profit.
We need to find the largest 4 digit number divisible by 77.
Largest 4 digit number = 9999.
The remainder when 9999 is divided by 77 is 66.
So answer is 9999 - 66= 9933.
Given that, N is a prime number we have to find 13N - 7.
9N is less than 180 and greater than 81 can be expressed as 81 < 9N < 180.
The above inequality can be simplified to get the term 13 - N as follows,
Dividing by 9, we get
9 < N < 20
Multiplying by 13 we get,
117 < 13N < 260.
Subtracting 7 from each term, we get
110 < 13N - 7 < 253
Therefore, 13N - 7 lies between 110 and 253.
From the given options, 164 is less than 233 and greater than 110.
Hence, the answer is 164.