1. In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?

a) 360

b) 280

c) 320

d) 330

Explanation: Let us assume there are 100 students in the institute.

Then, number of boys = 60

number of girls = 40

Further, 15% of boys get fee waiver = 9 boys

7.5% of girls get fee waiver = 3 girls

Total = 12 students who gets fee waiver

But, here given 90 students are getting fee waiver. So we compare

12 = 90

So, 1 = $$\frac{{90}}{{12}}$$ = 7.5

Now number of students who are not getting fee waiver = 51 boys and 37 girls

50% concession = 25.5 boys and 18.5 girls (i.e. total 44)

Required students = 44 × 7.5 = 330

2. After three successive equal percentage rise in the salary the sum of 100 rupees turned into 140 rupees and 49 paise. Find the percentage rise in the salary.

a) 12%

b) 22%

c) 66%

d) 82%

Explanain : Solve it through options

100 == 12% up ==> 112 == 12% up ==> 125.44 == 12% Up ==> 140.49

So, answer is 12%

3. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks then, the number of papers in which he got more than 50% marks is

a) 1

b) 3

c) 4

d) 5

Explanation: Let the marks obtained in five subjects be 6x, 7x, 8x, 9x and 10x.

Total marks obtained = 40x

Max. Marks of the five subjects = $$\frac{{40{\text{x}}}}{{0.6}}$$ [40x is 60% of total marks]

Max. Marks in each subject = $$\frac{{40{\text{x}}}}{{0.6 \times 5}}$$ = 13.33x

Hence, % of each subject = $$\frac{{6{\text{x}} \times 100}}{{13.33}}$$ = 45.01%

$$\frac{{7{\text{x}} \times 100}}{{13.33}}$$ = 52.51

In same way other percentage are 60.01%, 67.52%, 75.01%.

Number of subjects in which he gets more than 50% marks = 4

4. The length, breadth and height of a room are in ratio 3:2:1. If breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

a) remain the same

b) decrease by 13.64%

c) decrease by 15%

d) decrease by 30%

Explanation: Let length, breadth and height of the room be 3, 2, 1 unit respectively.

Area of walls = 2(l + b) × h = 2(3 + 2) × 1 = 10 sq. unit.

Now, length, breadth and height of room will become 6, 1 and $$\frac{1}{2}$$ respectively.

Area of walls = $$2\left( {6 + 1} \right) \times \frac{1}{2}$$ = 7 sq. unit.

% decrease in the area of walls = $$\left( {10 - 7} \right) \times \frac{{100}}{{10}}$$ = 30%

5. One bacterium splits into eight bacteria of the next generation. But due to environment, only 50% of one generation can produced the next generation. If the seventh generation number is 4096 million, what is the number in first generation?

a) 1 million

b) 2 million

c) 4 million

d) 8 million

Explanation: Let the number of bacteria in the 1

^{st}generation be x, then number of bacteria in 2

^{nd}, 3

^{rd}, 4

^{th}. . . . . Generation would be

$$8\left( {\frac{{\text{x}}}{2}} \right),\,8\left( {\frac{{4{\text{x}}}}{2}} \right),\,8\left( {\frac{{16{\text{x}}}}{2}} \right)$$ . . . . And so on.

As x, 4x, 16x, 64x . . . . . it is in GP with common ratio 4

Hence, 7th term of GP,

x(4)

^{6}= 4096

x = 1 or 1 million.

6. The price of raw materials has gone up by 15%, labor cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?

a) 28%

b) 17%

c) 27%

d) 24%

Explanation: Let the initial cost of raw material be 100. So, initial labor cost was 25 and net cost was 125

15% increment in raw materials cost and labor cost has gone up to 30% from 25 %

Raw material cost = 115

Labor cost = (115 × 30%) = 34.5

So, New net cost = 115 + 34.5 = 149.5

Difference of labor cost = 149.5 - 125 = 24.5

% reduction = $$\frac{{24.5 \times 100}}{{149.5}}$$ = 17%(approx.)

7. A sales executive gets 20% bonus of the total sales value and 10% commission besides the bonus on the net profit after charging such commission. If the total sales value be Rs. 10 lakh per annum and the total profit of the company be Rs. 1.32 lakh, then his total earning per annum will be, given that he is not entitled to receive any fixed salary from the company

a) 2.3 lakh

b) 2.32 lakh

c) 2.12 lakh

d) None of these

Explanation:

$$\eqalign{ & {\text{His bonus}}, \cr & = \frac{{ {20 \times 1000000} }}{{100}} \cr & = 2\, \text{lakh} \cr & {\text{Total}}\,{\text{profit}} = {\text{Net}}\,{\text{profit}} + \frac{{ {10 \times {\text{net}}\,{\text{profit}}} }}{{100}} \cr & 1.32\,\text{lakh} = {\text{Net}}\,{\text{profit}} \times \left[ {1 + {\frac{{10}}{{100}}} } \right] \cr & {\text{Net}}\,{\text{profit}} = \frac{{132000}}{{1.1}} = 120000 \cr & {\text{Commission}} = \left( {{\text{Total}}\,{\text{profit}} - {\text{Net}}\,{\text{profit}}} \right) \cr & = 132000 - 120000 \cr & = 12000 \cr & {\text{Hence}}, {\text{his}}\,{\text{total}}\,{\text{earnings}} \cr & = 2\,\text{lakh} + 12000 \cr & = Rs.\,212000 \cr} $$

8. A shepherd had n goats in the year 2000. In 2001 the no. of goats increased by 40%. In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew up 30%. In 2004, he sold 10% goats and then he had only 34,398 goats. The percentage increase of the no. of goats in this duration was :

a) 16.66%

b) 14.66%

c) 11.33%

d) 20%

Explanation: There is no need of the number of goats given i.e. 34,398.

Initially, let there be 100 goats.

100 == 40% ↑==> 140 == 30%↓(declined to 70%) ==> 98 == 30%↑ ==> 127.4 == 10%↓(sold) ==> 114.66

% increase = 14.66% [As 100 becomes 114.66]

9. In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1600 employees, then the no. of female employees who are computer literate ?

a) 690

b) 674

c) 672

d) 960

Explanation: Total employees = 1600

Female employees, 60% of 1600

$$ = \frac{{60 \times 1600}}{{100}} = 960$$

Then male employees = 640

50% of male are computer literate,

= 320 male computer literate

62% of total employees are computer literate,

$$ = \frac{{62 \times 1600}}{{100}} = 992$$ computer literate

Female computer literate = 992 - 320 = 672

10. The price of a car depreciates in the first year by 25% in the second year by 20% in third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Rs. 10,00,000 :

a) 7,80,000

b) 1,70,000

c) 6,90,000

d) 5,10,000

Explanation: Price after third depreciation,

100 ==25%↓ ==> 75 == 20%↓==>60 == 15% ↓ ==> 51

The price will be,

= Rs. 5,10,000