Direction [1-2]: Look carefully for the pattern, and then choose which pair of numbers comes next.
1. 42 40 38 35 33 31 28

A. 25 22 B. 26 23 C. 26 24 D. 25 23 E. 26 22

Answer: Option C
Explanation:
This is an alternating subtraction series in which 2 is subtracted twice, then 3 is subtracted once, then 2 is subtracted twice, and so on.
2. 6 10 14 18 22 26 30

A. 36 40 B. 33 37 C. 38 42 D. 34 36 E. 34 38

Answer: Option E
Explanation:
This simple addition series adds 4 to each number to arrive at the next.

1. In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

A. 2500 B. 2700 C. 2900 D. 3100 E. None of These

Answer: Option B
Explanation:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes = [latex] 7500 \times (\frac {80}{100})[/latex]
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = total valid votes [latex]\times (\frac {45}{100})[/latex]
[latex] 7500 \times (\frac {80}{100}) \times (\frac {45}{100}) = 2700[/latex]
2. If 20% of a = b, then b% of 20 is the same as :

A. 4% of a B. 6% of a C. 8% of a D. 10% of a E. None of these

Answer: Option A
Explanation:
20% of a = b
[latex] \Rightarrow (\frac {20}{100}) \times a = b [/latex]
b% of [latex]20 =(\frac {b}{100}) x 20 = [\frac {(\frac {20a}{100})} {100}] x 20 = \frac {4a}{100} = 4% of a.[/latex]

1. The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity?

A. 2010 B. 2011 C. 2012 D. 2013 E. None of These

Answer: Option B
Explanation:
Suppose commodity X wil cost 40 paise more than Y after Z years. Then,
(4.20 + 0.40Z) - (6.30 + 0.15Z) = 0.40
=> 0.25Z = 0.40 + 2.10 => Z= [latex] \frac {2.50}{0.25} = 10[/latex]
Therefore, X will cost 40 paise more than Y 10 years after 2001 . i.e in 2011
2. What will come in place of question mark in the following equation ? 54.(?)3 + 543 + 5.43 = 603.26

A. 6 B. 1 C. 9 D. 8 E. None of These

Answer: Option D
Explanation:
Let x + 543 + 5.43 = 603.26. Then, x = 603.26 - (543 + 5.43) = 603.26 - 548.43 =54.83
Missing digit = 8

1. The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is:

A. 10.5 B. 11.5 C. 12.5 D. 13.5 E. None of These

Answer: Option B
Explanation:
Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.
2. 10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is :

A. 1 B. 2 C. 3 D. 4 E. 10

Answer: Option C
Explanation:
Total age of 4 members, 10 years ago = (24 x 4) years = 96 years.
Total age of 4 members now = [96 + (10 x 4)] years = 136 years.
Total age of 6 members now = (24 x 6) years = 144 years.
Sum of the ages of 2 children = (144 - 136) years = 8 years.
Let the age of the younger child be x years.
Then, age of the elder child = (x+2) years.
So, x+(x+2) =8 x=3
Age of younger child = 3 years.

1. A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?

A. 15 B. 20 C. 10 D. 8 E. 25

Answer: Options C
Explanation:
Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = [latex] \frac {300}{x}[/latex]
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5([latex] \frac {300}{x}[/latex]) - 10x - 50 = 0 => −150 + [latex] {x}^{2} + 5x [/latex]
multiplying both sides by [latex] \frac {-1}{10x}[/latex]
=> [latex] {x}^{2} + 15x − 10x − 150 = 0 [/latex]
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
2. By how much is three-fifth of 350 greater than four-seventh of 210?

A. 90 B. 100 C. 110 D. 120 E. 25

Answer: Options A
Explanation:
[latex] \frac {3}{5} of 350 - \frac {4}{7} of 210 = 210 - 120 = 90.[/latex]

1. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present ?

A. 36 yrs B. 38 yrs C. 40 yrs D. 42 yrs E. None of These

Answer: Option C
Explanation:
Let the mother's present age be x years.
Then, the person's present age = [latex] \frac {2}{5}[/latex] x years.
[latex](\frac {2x}{5} + 8) = \frac {1}{2} (x + 8)[/latex]
[latex]2(2x + 40) = 5(x + 8) => x = 40.[/latex]
2. If Raj was one-third as old as Rahim 5 years back and Raj is 17 years old now, How old is Rahim now?

A. 40 B. 41 C. 36 D. 48 E. 50

Answer: Option B
Explanation:
Raj’s age today = 17 decades,
Hence, 5 decades back, he must be 12 years old.
Rahim must be 36 years old, Because (3×12).
5 years back Rahim must be 41 years old today. Because (36+5).

1. A trader sold an article at a loss of 5% but when he increased the selling price by Rs.65 he gained 3.33% on the cost price. If he sells the same article at Rs. 936, what is the profit percentage?

A. 15% B. 16.66% C. 20% D. data insufficient E. None of these

Answer: Option C
Explanation:
103.33 CP- 0.95 CP = 65
CP = Rs. 780
profit (%) = [latex]\frac {(936 - 780)}{780} x 100 = 20%[/latex]
2. Bhajan Singh purchased 120 reams of paper at Rs 80 per ream. He spent Rs 280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs 72 to the coolie. If he wants to have a gain of 8 %, what must be the selling price per ream?

A. 90 B. 89 C. 87.48 D. 86 E. None of these

Answer: Option A
Explanation:
Total investment = Rs. [latex](120 \times 80 + 280 + (\frac {40}{100}) \times 120 + 72)[/latex].
= Rs. (9600 + 280 + 48 + 72) = Rs, 10000.
Sell price of 120 reams = 108% of Rs. 10000 = Rs. 10800.
Sell Price per ream = Rs. [latex][\frac {10800}{120}] = Rs. 90.[/latex]

1. 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days ?

A. 15 days B. 11 days C. 14 days D. 12 days E. None of these

Answer: Option D
Explanation:
9M + 12B ----- 12 days ...........(1)
12M + 12B ------- 10 days........(2)
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)
From (1) & (3)
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days.
2. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

A. 215 days B. 225 days C. 235 days D. 240 days E. None of these

Answer: Option B
Explanation:
(10M + 15W) x 6 days = 1M x 100 days
=> 60M + 90W = 100M
=> 40M = 90W
=> 4M = 9W.
From the given data,
1M can do the work in 100 days
=> 4M can do the same work in [latex]\frac {100}{4}[/latex] = 25 days.
=> 9W can do the same work in 25 days.
=> 1W can do the same work in 25 x 9 = 225 days.
Hence, 1 woman can do the same work in 225 days.

1. A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.

A. 360, 160, 200 B. 160, 360, 200 C. 200, 360,160 D. 200,160,300 E. None of these

Answer: Option C
Explanation:
let ratio be x.
Hence no. of coins be 5x ,9x , 4x respectively
Now given total amount = Rs.206
=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206
we get x = 40
=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160
2. Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary?

A. 38000 B. 46800 C. 36700 D. 50000 E. None of these

Answer: Option A
Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,
[latex] \frac {(2x+4000)}{(3x+4000)} = \frac {40}{57} [/latex]
⇒ 57 × (2x + 4000) = 40 × (3x+4000)
⇒ 6x = 68,000
⇒ 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000

1. How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?

A. 4 years B. 2.5 years C. 3.5 years D. 2 years E. None of these

Answer: Option A
Explanation:
Time = [latex]\frac {(100 x 81)}{ (450 x 4.5)} = 4[/latex] years.
2. At what rate of compound interest per annum will a sum of rs.1200 becomes rs.1348.32 in 2 years

A. 66%% B. 6.5% C. 7% D. 7.5% E. None of these

Answer: Option A
Explanation:
rate = r%
[latex]1200 {(1 + \frac {r}{100})}^{2} = 1348.32[/latex]
r = 6%