Quant Boosters  Soumya Chakraborty  Set 3

After the 15% discount over 30, the new SP would have been 25.5.
But the shopkeeper returns a sachet worth rs. 1.5 to the customer, so the net SP = 24
CP = 24/1.2 = 20

Q9) A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

Profit of 100 = SP of 75
Thus, P/SP = 75/100
If P = 75, SP = 100, CP = 25
Thus, P/CP = 75/25, or 300%

Q10) The fees of a school increased 9.09%, then by 8.33%, and then by 7.69% over 3 years. If the current school fees is Rs. 3,360, then find the approximate school fees 3 years back.

The multiplication factors are:
9.09% increase = 12/11
8.33% increase = 13/12
7.69% increase = 14/13
So, the value becomes
(12/11) * (13/12) * (14/13) = 14/11
14 is the new part so that corresponds to 3360 = 14 * 240
11 should then correspond to 2640 (=11 * 240)

Q11) A student scored 43% in an exam and failed by 12 marks. Another student scored 48% marks in the same exam and passed by 18 marks. Find the passing percentage in the exam.

The percentage points difference is 5%, which corresponds to 30 marks
So each percentage point should be 6 marks. Now, someone who failed by 12 marks, must have failed 2 percentage points. As, he gets 43%, the passing percentage must be 45%

Q12) In September 2009, the sales of a product were 2/3rd of that in July 2009. In November 2009, the sales of the product were higher by 5% as compared to September 2009. How much is the percentage of increase in sales in November 2009 with respect to the base figure in July 2009.

5% increase = 21/20
So, effectively = (2/3) * (21/20) = 7/10, which implies a reduction of 3/10 = 30% decrease

Q13) The length, breadth and height of a room are in ration 3:2:1. The breadth and height of the room are halved and length of the room is doubled. Then area of the four walls of the room will
a) Decrease by 13.64%
b) Decrease by 15%
c) Decrease by 18.75%
d) Decrease by 30%

I don't like unnecessary fractions. As we are about to half the breadth and height, so let us keep these two values EVEN number to begin with
Length = 6
Breadth = 4
Height = 2
Area of the four walls, initially = (6+4) * 2 * 2 = 40
New values
L = 12
B = 2
H = 1
Area of four walls, new = (12+2) * 1 * 2 = 28
Reduction = 12/40 = 30%

Q14) The difference between the value of a number increased by 25% and the value of the original number decreased by 30% is 22. What is the original number?

Increased by 25%, multiplication factor of 5/4
Reduced by 30%, multiplication factor of 7/10
As, we are dealing with the same number, let us find the difference between these two fractions
5/4  7/10 = 25/20  14/20 = 11/20
11 corresponds to 22
Thus, 20 corresponds to 40
I have purposely added few extra steps to enable you to understand how i calculate these mentally

Q15) Wheat is now being sold at Rs 27 per kg. During last month its cost was rs 24 per kg. Find by how much percent a family reduces its consumption so as to keep the expenditure fixed.

Just reverse the multiplying factor here.
AS the price becomes 27/24 = 9/8
The consumption must become 8/9 to keep the expenditure constant
So, the reduction must be 1/9 = 11.11%
You can also treat this as a proportionality question, where price and consumption are inversely proportional.

Q16) For how many values of 'n' in the range of 1 to 1000, does 2^(2^n) when divided by (2^n  1) leave a remainder of 1 ?

If 2^(2^n) when divided by 2^n  1 leaves a remainder of 1
It implies that 2^(2^n)  1 must be divisible by 2^n  1
a^x  b^x is divisible by a^y  b^y, only if x is divisible by y
Thus in the question 2^n must be divisible by n
Only possible if n is also a power of 2
You can't consider n = 2^0 = 1
In that case 2^n  1 = 1
If the divisor is 1, that can't leave a remainder
So in the range we have, 2^1 to 2^9 ... Nine possibilities

Q17) A bakery opened with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 60% of the remaining rolls were sold between noon and closing time. How many dozen rolls were left unsold?

50% + 60% of 50% are gone = 80% gone
left with 20% of 40 = 8

Q18) If (3x+2y)/(3x2y) = 5/2, Find (5x+4y)/(7x2y)