Question 1. Twice The Speed Of A Boat Downstream Is Equal To Thrice The Speed Upstream. The Ratio Of Its Speed In Still Water To The Speed Of Current Is
Let the boat speed in nonetheless water be b.
Let the circulate speed be x.
2(b+ x) = three(b-x)
Question 2. A Person Has A Chemical Of Rs. 25 Per Litre. In What Ratio Should Water Be Mixed With That Chemical So That After Selling The Mixture At Rs. 20/litre He May Get A Profit Of 25% ?
This may be solved the use of alligation.
What is required at the end of mixing is a charge of 20/1.25 = sixteen.
So the alligation could appear like this –
Water/zero Mixture/sixteen Chemical/25
Hence the ratio might be (25 – 16) : sixteen = nine : 16
Hence required ratio of Water : Chemical is nine:16.
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Question 3. The Difference Between The Simple Interest And Compound Interest On A Certain Sum Of Money For 2 Years At 15% P. A. Is Rs. 45. Find The Sum ?
Since we realize that the hobby rate is 0.15, and knowing that the difference between years of compound hobby is not anything however hobby on interest, we are able to locate the primary yr’s interest as –
45/0.15 = 300.
Now if the interest is three hundred on the cease of 12 months, then the main is 300 / 0.15 = 2,000
Question four. How Many Terms Are There In An A.P. Whose First And Fifth Terms Are -14 And 2, Respectively, And The Sum Of Terms Is forty ?
Now the common distinction of this AP is 16/four = 4.
The sum of an AP is n/2 2a + (n – 1)d
Substituting we get, 40 = n/2 2×-14 + (n – 1)four
The quality manner to solve this is with the aid of plugging alternatives. Put in n = 10 and get the RHS as 40.
Question 5. In A Class, 50 Students Play Cricket, 20 Students Play Football And 10 Play Both Cricket And Football. How Many Play At Least One Of These Two Games ?
The required answer is 50 + 20 – 10 = 60.
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Question 6. A Bottle Is Full Of Dettol. One-0.33 Of It Is Taken Out And Then An Equal Amount Of Water Is Poured Into The Bottle To Fill It. This Operation Is Done Four Times. Find The Final Ratio Of Dettol And Water In The Bottle ?
As in denominator we should take 1/three four instances so, we begin through assuming 81 ml of dettol within the bottle. After the first new release you may be left with
2/three × 81 = fifty four ml. After the second generation you will be left with
2/3 × 54 = 36 ml. After the 0.33 new release you'll be left with
2/three × 36 = 24 ml. After the fourth generation you'll be left with
2/three × 24 = sixteen ml. So the specified ratio can be 16 : (81 – 16) = 16 : sixty five
Question 7. In A Survey Of Defaulted Payments Of Electrical Bills Of A Residential Complex Of one hundred twenty five Houses, It Is Found That 50 Houses Defaulted On Their Payment Of Electrical Bills In January, 60 In February And 40 In March. Houses Can Default In Consecutive Months Only. 20 Defaulted In January And February. 10 Defaulted In February And March. How Many Houses Defaulted In All The three Months?
We use method for intersection of 3 sets, preserving in mind that Jan ∩ Mar does no longer exist, due to the fact that they may be not consecutive months.
Let x be the quantity of human beings defaulting in all three months.
We get the equation as : a hundred twenty five = 50 + 60 + 40 – 20 – 10 + x. Solving we get x = five.
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Question 8. India Plays Two Matches Each With West Indies And Australia. In Any Match The Probabilities Of India Getting Points 0, 1, 2 Are zero.45, 0.05 And 0.50 Respectively. Assuming That Outcomes Are Independent, The Probability Of India Getting At Least 7 Points Is
Getting 7 factors is possible in 2 cases.
Case 1: India wins all 4 suits.
Probability: (.5)four = .0625.
Case 2: India wins any of the three fits and attracts the ultimate fit. This can take place in overall 4 methods. Probability: 4 x (.50)3 x (.05) = .0.5.
So, required chance: .0625 + .1/2 = .0875
Question 9. In Order To Obtain An Income Of Rs. 650 From 10% Stock At Rs. Ninety six, One Must Make An Investment Of
To achieve Rs. 10, investment = Rs. 96.
To achieve Rs. 650, investment = Rs.Ninety six/10x 650 = Rs. 6240.
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Question 10. Express A Speed Of 36 Kmph In Meters Per Second ?
36 * five/18 = 10 mps
Question eleven. Express 25 Mps In Kmph?
25 * 18/5 = ninety kmph
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Question 12. A Boy Has Nine Trousers And 12 Shirts. In How Many Different Ways Can He Select A Trouser And A Shirt?
The boy can select one trouser in nine approaches.
The boy can pick one shirt in 12 methods.
The number of approaches wherein he can pick one trouser and one blouse is 9 * 12 = 108 ways.
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Question 13. How Many Three Letter Words Are Formed Using The Letters Of The Word Time ?
The variety of letters within the given word is 4.
The number of 3 letter words that can be formed the use of those 4 letters is ?P? = 4 * 3 * 2 = 24.
Question 14. Using All The Letters Of The Word "thursday", How Many Different Words Can Be Formed ?
Total range of letters = 8
Using these letters the quantity of 8 letters phrases formed is ?P? = 8!.
Question 15. Using All The Letters Of The Word "nokia", How Many Words Can Be Formed, Which Begin With N And End With A ?
There are five letters within the given phrase.
Consider 5 blanks .
The first clean and last blank have to be full of N and A all the closing three blanks may be packed with the closing three letters in 3! Ways.
The wide variety of words = three! = 6.
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Question sixteen. The Number Of Arrangements That Can Be Made With The Letters Of The Word Meadows So That The Vowels Occupy The Even Places ?
The word MEADOWS has 7 letters of which three are vowels.
As the vowels must occupy even places, they can be organized within the three even locations in 3! I.E., 6 methods. While the consonants can be organized amongst themselves within the ultimate 4 locations in 4! I.E., 24 approaches.
Hence the total ways are 24 * 6 = a hundred and forty four.
Question 17. The Number Of Permutations Of The Letters Of The Word 'mesmerise' Is_.
n gadgets of which p are alike of 1 kind, q alike of the alternative, r alike of another kind and the closing are distinct can be organized in a row in n!/p!Q!R! Methods.
The letter sample 'MESMERISE' includes 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements = nine!/(2!)2 3!
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Question 18. A Committee Has 5 Men And 6 Women. What Are The Number Of Ways Of Selecting 2 Men And 3 Women From The Given Committee ?
The range of approaches to pick guys and 3 girls = ?C? * ?C?
= (five *four )/(2 * 1) * (6 * 5 * four)/(3 * 2)
= two hundred
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