**Question 1. An Article When Sold At A Gain Of 5% Yields Rs. 15 More Than When Sold At A Loss Of 5%. The Cost Price Of The Article Is:****Answer :**10/100 × x = 15 ⇒ x=150

As the loss and profit both are earned on the cost price.

**Question 2. If X Gets 25% More Than Y And Y Gets 20% More Than Z, The Share Of Z Out Of Rs. 740 Will Be:****Answer :**Z share = Z,

Y = 1.2Z

X = 1.25×1.2Z,

X+Y+Z =740

(1.25× 1.2+1.2+1)Z=740

3.7Z=740, Z=200

**Question 3. In A Mixture Of 35 Litres The Ratio Of Milk And Water Is 4 : 1. If 7 Litres Of Water Is Added To The Mixture, The Ratio Of Milk To Water In The Resultant Mixture Will Become :****Answer :**Mixture = 35L, Milk = 4/5 × 35 =28L

Water = 1/5 × 35 =7L

New 28/7+7 = M/W

⇒ 28/14 = M/W =2/1

**Question 4. What Will Be The Income Tax Payable By A Person Getting A Taxable Income Of Rs. 30,000 During The Year If The First Rs. 18000 Is Not Taxable And The Tax Rates Are 25% Of The Next Rs. 12000 ?****Answer :**T.I.=30,000, N.T.I.=18000

Taxable 12000, Income Tax = 25% of Taxable Income

= 1/4 ×: 12000 = RS.3000

**Question 5. 10 Men Can Finish A Piece Of Work In 10 Days Whereas It Takes 12 Women To Finish It In 10 Days. If 15 Men And 6 Women Undertake To Complete The Work, How Many Days Will They Take To Complete The Work?****Answer :**10 men = 10 days, 1 men 1 day = 1/100 work

12 women = 12 days, 1 women 1 day = 1/120

15 men + 6 women, 15 × 1/100 + 6 × 1/120

3/20 +1/20= 4/20 =1/5 work= 5 days

**Question 6. A Merchant Marks His Wares 40% More Than The Real Price And Allows 20% Discount. His Profit Is:****Answer :**Let the CP = 100 Rs.

Mark Price = 140

Discount = 20%

Selling price 80/100 × 140 = 112

Hence profit = 12%

**Question 7. A Person Spends 40% Of His Salary On Food, 25% On House Rent, 15% On Entertainment And 5% On Conveyance. If His Savings At The End Of The Month Is Rs. 1200, Then His Salary Per Month In Rupees Is:****Answer :**Total expenditure = 40 + 25 + 15 + 5 = 85%

Saving = (100 – 85) = 15%

15/100 × Salary = 1200, Salary = 8000 Rs.

**Question 8. The Difference Between Ages Of A Man And His Daughter Is 28. The Average Of Their Ages Now Is 28. What Are Their Present Ages?****Answer :**Let the daughter’s current age be x.

The current age of father = 28+x

According to the question, the averages of their ages is 28.

Hence, (x+28+x)/2 =28

X =14.

Therefore, the daughter’s present age is 14 and the father’s present age is 42

**Question 9. The Heights Of Five Runners Are 160 Cm, 137 Cm, 149 Cm, 153 Cm And 161 Cm Respectively. Find The Mean Height Per Runner.**

Solution:**Answer :**Mean height = Sum of the heights of the runners/number of runners

= (160 + 137 + 149 + 153 + 161)/5 cm

= 760/5 cm

= 152 cm.

Hence, the mean height is 152 cm.

**Question 10. Find The Mean Of The First Five Prime Numbers.****Answer :**The first five prime numbers are 2, 3, 5, 7 and 11.

Mean = Sum of the first five prime numbers/number of prime numbers

= (2 + 3 + 5 + 7 + 11)/5

= 28/5

= 5.6

Hence, their mean is 5.6

**Question 11. Find The Mean Of The First Six Multiples Of 4.****Answer :**The first six multiples of 4 are 4, 8, 12, 16, 20 and 24.

Mean = Sum of the first six multiples of 4/number of multiples

= (4 + 8 + 12 + 16 + 20 + 24)/6

= 84/6

= 14.

Hence, their mean is 14.

**Question 12. Find The Arithmetic Mean Of The First 7 Natural Numbers.****Answer :**The first 7 natural numbers are 1, 2, 3, 4, 5, 6 and 7.

Let x denote their arithmetic mean.

Then mean = Sum of the first 7 natural numbers/number of natural numbers

x = (1 + 2 + 3 + 4 + 5 + 6 + 7)/7

= 28/7

= 4

Hence, their mean is 4.

**Question 13. If The Mean Of 9, 8, 10, X, 12 Is 15, Find The Value Of X.****Answer :**Mean of the given numbers = (9 + 8 + 10 + x + 12)/5 = (39 + x)/5

According to the problem, mean = 15 (given).

Therefore, (39 + x)/5 = 15

⇒ 39 + x = 15 × 5

⇒ 39 + x = 75

⇒ 39 – 39 + x = 75 – 39

⇒ x = 36

Hence, x = 36.

**Question 14. The Mean Of 40 Numbers Was Found To Be 38. Later On, It Was Detected That A Number 56 Was Misread As 36. Find The Correct Mean Of Given Numbers.****Answer :**Calculated mean of 40 numbers = 38.

Therefore, calculated sum of these numbers = (38 × 40) = 1520.

Correct sum of these numbers

= [1520 – (wrong item) + (correct item)]

= (1520 – 36 + 56)

= 1540.

Therefore, the correct mean = 1540/40 = 38.5.

**Question 15. The Mean Of The Heights Of 6 Boys Is 152 Cm. If The Individual Heights Of Five Of Them Are 151 Cm, 153 Cm, 155 Cm, 149 Cm And 154 Cm, Find The Height Of The Sixth Boy.****Answer :**Mean height of 6 boys = 152 cm.

Sum of the heights of 6 boys = (152 × 6) = 912 cm

Sum of the heights of 5 boys = (151 + 153 + 155 + 149 + 154) cm = 762 cm.

Height of the sixth boy

= (sum of the heights of 6 boys) – (sum of the heights of 5 boys)

= (912 – 762) cm = 150 cm.

Hence, the height of the sixth girl is 150 cm.

**Question 16. A Train Running At The Speed Of 60 Km/hr Crosses A Pole In 9 Seconds. What Is The Length Of The Train ?****Answer :**Length of the train = (Speed x Time) =50/3 x 9 m = 150 m.

**Question 17. A, B, C Are Partners In A Business. During A Particular Year. A Received One Third Of The Profit. B Received One Fourth Of The Profit And C Received The Remaining Rs. 5000. How Much Amount Of Money Did A Receive ?****Answer :**Lets assume Total profit x

x * (1-1/3-1/4) = 5000

=> x*(12-4-3)/12 = 5000

x = 5000*12/5 = Rs. 12000

so A’s share = Rs. (1/3*12000) = Rs. 4000

**Question 18. A Man Owns 2/3 Of The Market Research Beauro Business And Sells 3/4 Of His Shares For Rs. 75000. What Is The Value Of Business ?****Answer :**3/4 of his share = 75000

so his share = 100000.

2/3 of business value = 100000

so total value = 150000

**Question 19. A Train Running At Speed Of 126 Kmph. What Will Be The Length Of Train If It Cross A Tree In 5 Sec.****Answer :**Formula Used: Distance = (Speed * Time)

convert the train speed (Kmph) in to mps multiply by 5/18

speed (mps) = 126 * 5/18 = 35 mps

length = ( 35 * 5 ) meter

= 175 meter

**Question 20. 320m Long Train Is Running At 72 Kmph. How Much Time It Will Take To Cross A Platform Of 180m Long ?****Answer :**Total Length = Platform Length + Train Length

So Total Length = 500m

convert the train speed (Kmph) in to mps multiply by 5/18

speed (mps) = 72 * 5/18 = 20mps

Formula Used: Time = Distance/Speed

Time = (500 / 20 ) sec

= 25 sec

**Question 21. Anirudh, Harish And Sahil Invested A Total Of Rs.1,35,000 In The Ratio 5:6:4 Anirudh Invested Has Capital For 8 Months. Harish Invested For 6 Months And Sahil Invested For 4 Months. If They Earn A Profit Of Rs.75,900,then What Is The Share Of Sahil In The Profit ?****Answer :**Anirudh invest for 8 months,haris invested for 6 and

sahil for 4 months in the ratio of 5:6:4

so ratio = 5*8 : 6*6 : 4*4

=> 40:36:16

=> 10:9:4

So sahil’s profit=(4/23)*75900 = 13200

**Question 22. A Train Overtakes Two Persons Who Are Walking In The Same Direction In Which The Train Is Going, At The Rate Of 2 Kmph And 4 Kmph And Passes Them Completely In 19 And 20 Seconds Respectively. The Length Of The Train Is:****Answer :**Convert the persons Speed in m/sec

2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.

4 kmph = (4 x 5/18 m/sec = 10/9 m/sec.

Let the length of the train be x meters and its speed by y m/sec.

Relative speed in respect to both person (y – 5/9) and (y – 10/9)

Formula Used: Time = Distance / speed

so x / (y – 5/9) = 19 —- (1)

and x / (y – 10/9) = 20 —- (2)

9x = 19 (9y – 5) —– (1)

9x = 20 (9y – 10) ——(2)

find the value of x and y

19 (9y – 5) = 20(9y – 10)

171 y – 95 = 180 y -200 => 9y = 105 => y = 105/9 = 35/3

Now find the value fo x by above any equations

9x = 171 *35/3 – 95 = 57 *35 – 95

9x = 1900 => x = 211.1 meter

**Question 23. Ajay, Vijay And Sanjay Rent A Pasture. Ajay Puts 10 Oxen For 7 Months, Vijay Puts 12 Oxen For 5 Months And Sanjay Puts 15 Oxen For 3 Months For Grazing. If The Rent Of The Pasture Is Rs. 175, How Much Must Sanjay Pay As His Share Of Rent ?****Answer :**Ajay : Vijay : Sanjay = 10 * 7 : 12 * 5 : 15 * 3

= 70 : 60 : 45 = 14 : 12 : 9.

So Sanjay’s rent = Rs. (175 * 9/35) = Rs. 45.

**Question 24. A Train Overtakes Two Persons Walking Along A Railway Track. The First One Walks At 4.5 Km/hr. The Other One Walks At 5.4 Km/hr. The Train Needs 8.4 And 8.5 Seconds Respectively To Overtake Them. If Both The Persons Are Walking In The Same Direction As The Train? So What Is The Speed Of The Train ?****Answer :**Convert the Speed in m/sec

so 4.5 km/hr = ( 4.5 x 5/18 ) m/sec = 5/4 m/sec = 1.25 m/sec,

and 5.4 km/hr = ( 5.4 x 5/18 ) m/sec = 3/2 m/sec = 1.5 m/sec.

Here assume the speed of the train as x m/sec.

so relative will be (x-1.25) and (x – 1.5)

(x – 1.25) x 8.4 = (x – 1.5) x 8.5

=> 8.4x – 10.5 = 8.5x – 12.75

=> 0.1x = 2.25

=> x = 22.5 m/s

As options are given in km/hr so convert the speed mps to kmph

So Speed of the train = ( 22.5 x 18/5 ) km/hr = 81 km/hr.

**Question 25. X And Y Started A Business Together. If X Invested Rs. 16,000 For 8 Months And Y Invested Some Amount In The Business For 4 Months. If Y Claims 2/7 Of The Total Profit Earned. How Much Money Was Invested By Y?****Answer :**Lets assume the total profit = Rs. T

so Y part = 2*T/7 and

X part = T – 2*T/7 = 5*T/7

X, Y ratio

=> X : Y = 5*T/7 : 2*T/7 = 5 : 2

Y invested Rs.P

so (16000 * 8) / (P * 4) = 5/2

=> P = (16000 * 8 * 2) /(5 * 4)

=> P = Rs. 12800

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