**Question 1. A Train 110 M Long Is Running With A Speed Of 60 Km/hr. In What Time Will It Pass A Man Who Is Running At 6 Km/hr In The Direction Opposite To That In Which The Train Is Going ?****Answer :**Speed of train relative to man = 60 + 6 = 66 km/hr.

= 66 * 5/18 = 55/3 m/sec.

Time taken to pass the men = 110 * 3/55 = 6 sec.

**Question 2. Ram Bought 4 Dozen Apples At Rs. 12 Per Dozen And 2 Dozen Apples At Rs. 16 Per Dozen. He Sold All Of Them To Earn 20%. At What Price Per Dozen Did He Sell The Apples ?****Answer :**6 dozen apples = Rs. (12 × 4 + 16 × 2) = Rs. 80

Gain = 20%

S.P = Rs. (120/100 × 80) = Rs. 96

Per dozen = Rs. (96/6) = Rs. 16

**Question 3. In A Game Of 90 Points A Can Give B 15 Points And C 30 Points. How Many Points Can B Give C In A Game Of 100 Points ?****Answer :**While A scores 90 points, B scores (90-15)=75 points and C scores (90-30)= 60 points

i.e., when B scores 75 points, C scores 60 points

=> When B scores 100 points, C scores 6075×100 = 80 points

i.e., in a game of 100 points, B can give C (100-80)=20 points

**Question 4. 150 Men Consume 1050 Kg Of Rice In 30 Days. In How Many Days Will 70 Men Consume 980 Kg Of Rice?****Answer :**Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day

Let us say 70 men take x days to consume 150 kg.

Quantity consumed by each item in x days = (7x/30) kg

Quantity consumed by 70 men in x days = (7/30 x)(70) kg

= (7/30 x) * (70) = 960

x = 60 days.

**Question 5. 22004 – 29303 + 101299 – 59532 = ?****Answer :**22004 – 29303 + 101299 – 59532

123303 – 888.35 = 34468 = 34500

**Question 6. A Alone Can Do A Piece Of Work In 6 Days And B Alone In 8 Days. A And B Undertook To Do It For Rs. 3200. With The Help Of C, They Completed The Work In 3 Days. How Much Is To Be Paid To C ?****Answer :**C’s 1 day’s work = 1/3 – (1/6 + 1/8) = 1/3 – 7/24 = 1/24

A’s wages : B’s wages : C’s wages

1/6 : 1/8 : 1/24 = 4:3:1

C’s share = 1/8 * 3200 = Rs. 400

**Question 7. In Digging A Pond 20 M * 10 M * 5 M The Volumes Of The Soil Extracted Will Be ?****Answer :**20 * 10 * 5 = 1000

**Question 8. The Greatest Number Of Four Digits Which Is Divisible By 15, 25, 40 And 75 Is:****Answer :**Greatest number of 4-digits is 9999.

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

Required number (9999 – 399) = 9600.

**Question 9. The Product Of Two Numbers Is 4107. If The H.c.f. Of These Numbers Is 37, Then The Greater Number Is:****Answer :**Let the numbers be 37a and 37b.

Then, 37a x 37b = 4107

ab = 3.

Now, co-primes with product 3 are (1, 3).

So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).

Greater number = 111.

**Question 10. A Person Crosses A 600 M Long Street In 5 Minutes. What Is His Speed In Km Per Hour ?****Answer :**Speed = 600/ 5 x 60 m/sec. = 2 m/sec. = 2 x 18/5km/hr =7.2 km/hr

**Question 11. Worker A Takes 8 Hours To Do A Job. Worker B Takes 10 Hours To Do A Job. How Long Should It Take Both A And B, Working Together To Do The Same Job ?****Answer :**first we need to calculate 1 hours work, then their collective work as A’s 1-hour work is 1/8

B’s 1-hour work is 1/10

(A+B)’s 1 hour work = 1/8 + 1/10= 9/40

So both will finish the work in 40/9 hours=4 4/9

**Question 12. A And B Started A Business By Investing Rs.4000/- And Rs.5000/- Respectively. Find The A’s Share Out Of A Total Profit Of Rs.1800:****Answer :**A = Rs.4000/-

B = Rs.5000/-

A share 4 parts & B share 5 parts

Total 9 parts —–> Rs.1800/-

—-> 1 part ——-> Rs.200/-

A share = 4 parts —–> Rs.800/-

**Question 13. A Mixture Contains Alcohol And Water In The Ratio 4 : 3. If 5 Liters Of Water Is Added To The Mixture, The Ratio Becomes 4: 5. Find The Quantity Of Alcohol In The Given Mixture.****Answer :**Let the quantity of alcohol and water be 4x litres and 3x litres respectively

4x/(3x+5) = 4/5

20x = 4(3x+5)

8x = 20

x = 2.5

Quantity of alcohol = (4 x 2.5) litres = 10 litres.

**Question 14. A Boat Can Travel With A Speed Of 13 Km/hr In Still Water. If The Speed Of The Stream Is 4 Km/hr, Find The Time Taken By The Boat To Go 68 Km Downstream.****Answer :**Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream =68/17hrs = 4 hrs.

**Question 15. Sam And Joan Are Playing A Tennis Match. If The Probability Of Sam’s Win Is 0.59, Then Find The Probability Of Joan’s Win.****Answer :**Let event A = Sam wins and event B = Joan wins. Then,

P(A) = 0.59

Since if Sam wins, Joan cannot win and if Joan wins, Sam cannot win, so we can say that the events A and B are mutually exclusive. Other than these two events, there are

no any other possible outcomes. So,

P(A)+P(B) = 1

0.59+P(B) = 1

P(B) = 1-0.59 = 0.41

**Question 16. The Ratio Between The Length And The Breadth Of A Rectangular Park Is 3: 2. If A Man Cycling Along The Boundary Of The Park At The Speed Of 12 Km/hr Completes One Round In 8 Minutes, Then The Area Of The Park (in Sq. M) Is:****Answer :**Perimeter = Distance covered in 8 min. =12000x 8m = 1600 m.

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

Length = 480 m and Breadth = 320 m.

Area = (480 x 320) m2 = 153600 m2.

**Question 17. The Average Of Runs Of A Cricket Player Of 10 Innings Was 32. How Many Runs Must He Make In His Next Innings So As To Increase His Average Of Runs By 4?****Answer :**Average = total runs / no.of innings = 32

So, total = Average x no.of innings = 32 x 10 = 320.

Now increase in avg = 4runs. So, new avg = 32+4 = 36runs

Total runs = new avg x new no. of innings = 36 x 11 = 396

Runs made in the 11th inning = 396 – 320 = 76

**Question 18. The Greatest Number Which On Dividing 1657 And 2037 Leaves Remainders 6 And 5 Respectively, Is:****Answer :**Required number = H.C.F. of (1657 – 6) and (2037 – 5)

= H.C.F. of 1651 and 2032 = 127.

**Question 19. Two Pipes A And B Can Fill A Tank In 20 And 30 Minutes Respectively. If Both The Pipes Are Used Together, Then How Long It Will Take To Fill The Tank ?****Answer :**we first get the filling in 1 minute for both pipes then we will add them to get the result, as

Part filled by A in 1 min = 1/20

Part filled by B in 1 min = 1/30

Part filled by (A+B) in 1 min = 1/20 + 1/30= 1/12

So both pipes can fill the tank in 12 mins.

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