A student was asked to multiply a number by 3/2 but he divided that number by 3/2. The result was therefore 10 less then the correct answer. Find the number.

Let the number be N
According to the question 5N = 2N² - 3
? 2N² - 5N -3 = 0
? (N - 3) (2N + 1) = 0
N = 3 & -1/2
Thus the required number is 3

Given Exp. = (a²+ b²+ ab) / (a³-b³)
= 1 / (a - b)
= 1 / (16 - 5)
= 1/11.

Let the five consecutive number are N - 2, N - 1, N, N +1, N+2
Sum of numbers = 190
? N-2 + N -1 + N + N + 2 = 190
? 5N = 190
? N = 38
Sum of largest and smallest numbers = (N + 2) + (N - 2)
= 2N = 2 x 38
= 76

Let the unit digits of the number be N and 10s digit be M
? Number = 10M + N

According to the question
MN = 10 .......(i)
And 10N + M = (10M + N) - 36
? 10N + M - 10M - N = -36
? 9N - 9M = - 36
? N - M = -4 .......(2)
On Adding eq. (i) and (ii) we get
N + M = 10
N - M = - 4
2N = 6
? N = 3 and M = 7
? Required product of two digits = 3 x 7 = 21

Let d = divisor and q = quotient

First remove the last remainder:
d x q + 413 = 380606
d x q = 380193

So d cannot be even (choice d) or a multiple of 5 (choice c).

If we try choice a or b,
a quick division (by calculator) shows that
380193 = 451 x 843, the other two choices.

(In the absence of choices, we could find the prime factors of 380193,
which are 3 x 11 x 41 x 281 and get various candidate divisors from that.)

So one of them is the divisor and the other the quotient.

So we can just check the first remainder:
843 x 4 = 3372
3806 - 3372 = 434 ... a match!

And just to be sure:
451 x 8 = 3608
3806 - 3608 = 198

So the divisor is 843.

Sum of the five consecutive odd number = N + (N + 2) + (N + 4) + (N + 6) + (N + 8) =175
? 5N + 20 =175
? N = (175 - 20) / 5 = 31

Sum of the second largest and square of smallest one = (31 + 6) + (31)²
= 37 + 961=998

let the total number of sweet = N
According to the question
(N/250) - (N/300) = 1
? (6N - 5N) / 1500=1
? N = 1500

Let the number be P and Q
According to the question
(P + Q) = 2.5 (P - Q)
? P + Q = 2.5P - 25Q
? 3.5Q = 1.5P
? P / Q = 7/3 .....(i)
Now PQ = 84
? Q² = (84 x 3) / 7
? Q² = 36
? Q = 6
&ther4; P = (7/3) x 6 = 14

Sum of the number = P + Q = 14 + 6 = 20

Let the third number = N
Then the first number = 3N
And second number = 3N/2
According to the question [N + 3N + 3N/2] / 3=154
? (2N +6N +3N) / 6 = 154
? N = (154 x 6) / 11 = 84
? Required difference = 3N - N = 2N
= 2 x 84 = 168

Number of trees that can be planted on one side of road = (1760 / 20) + 1
= 88 + 1
=89

? Trees on the both side = 2 x 89=178