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Given:

Sum of 3 numbers = 136

First number : Second number = 2 : 3

Second number : Third number = 5 : 3

Concept used:

If the ratio of A : B and B : C is given 

Then, to find ratio of A : B : C

To make ratio of B equal we have to apply the formula below.

A : B₁ and B₂ : C

A : B : C = A × B₂ : B₁ × B₂ : B₂ × C

Calculation:

Let the first, second and third numbers be A,B and C respectively.

⇒ A + B + C = 136

A : B = 2 : 3

B : C = 5 : 3

⇒ A : B : C = 10 : 15 : 9

⇒ A + B + C = 10x + 15x + 9x

⇒ A + B + C = 34x

⇒ 34x = 136

⇒ x = 4

⇒ B = 15x 

⇒ B = 60

∴ The second number is 60.

Given:

15 men complete a piece of work in 21 × 8 hours

work done by 3 women = work done by 2 men

Formula used:

Total work = Efficiency × time

If the total work is constant. then,

Efficiency ∝ TIme

By reversing the time we get ratio of efficiency.

Calculation:

First we need to find efficiency

work done by 3 women = work done by 2 men

⇒ Women : Men = 2 : 3

Men total efficiency = 3 × 15 = 45

Total work = 45 × 21 × 8

Time taken by 21 women working 6 hours a day

Efficiency of 21 women = 21 × 6 × 2

Time = Total work/Efficiency

⇒ (45 × 21 × 8)/(21 × 6 × 2)

⇒ 30 days

∴ 21 women woking 6 hours a day will take 30 days to complete a peice of work.

Given:

Length of the train = 100 meters

Speed of the train = 36 km/hr

Formula used:

Speed = Distance/Time

To convert km/hr into m/s multiply by 5/18

Calculation:

First, convert km/hr into m/s

⇒ 36 × (5/18) = 10 m/s

Speed = Distance/Time

⇒ 10 = 100/time

⇒ time = 10 seconds

∴ The time taken by the train to pass the telegraph post is 10 seconds.

Given:

'A' completes a piece of work = 12 days

A and B together complete a piece of work = 8 days

Concept used:

If a person does work in 'n' days then in one day a person does 1/n part of the total work.

Calculation:

One day work by A + one day work by B = one day work by both A and B

1/A + 1/B = 1/(A +B)

⇒ 1/12 + 1/B = 1/8

⇒ 1/B = (1/8) –(1/12)

⇒ 1/B = (3 –2)/24

⇒ 1/B = 1/24

⇒ B = 24 

∴ 'B' can  alone complete the same piece of work in 24 days.

Given:

The sum of two digits of a two digits number = 12

And the difference between the two digits of the two digits number = 6

Calculation:

First condition:

Let us assume numbers be xy. and we assume x is greater than y

According to question;

x + y = 12       ----(i)

And x – y = 6      ----(ii)

After adding equation (i) and (ii), we get,

2 × x = 12 + 6

⇒ 2x = 18

⇒ x = 18/2

⇒ x = 9

Put x = 9 in equation (i) we get,

9 + y = 12

⇒ y = 12 – 9

⇒ y = 3

Number xy that is 93.

Second condition:

Let us assume numbers be xy. and we assume y is greater than x

According to question;

x + y = 12       ----(i)

and y – x = 6      ----(ii)

After adding equation (i) and (ii), we get,

2 × y = 12 + 6

⇒ 2y = 18

⇒ y = 18/2

⇒ y = 9

Put y = 9 in equation (i) we get,

9 + x = 12

⇒ x = 12 – 9

⇒ x = 3

Number xy that is 39.

The above two values will be possible but in the option 93 is only given so we choose the two-digit number as 93.

∴ The two-digit number is 93.

Given:

Five bells commence tolling together and toll at intervals of 9, 6, 4, 10 and 8 seconds respectively.

Concept used:

Least common multiplication 

Calculation:

A least common multiple of (9, 6, 4, 10 and 8)

We can write 9 = 3²

4 = 22 

6 = 2 × 3

8 = 23 

10 = 2 × 5

A least common multiple of (9, 6, 4, 10 and 8) = 23 × 3² × 5

⇒ 8 × 9 × 5

⇒ 360 sec

Bells ring together after every 360 sec 

Required number of times in 1 hour (60 × 60 seconds) = [(60 × 60)/360]

⇒ 10

But we have to add 1 because at starting all bells will be rung once a time after that the ring 10 times.

⇒ 10 + 1 

⇒ 11 times 

∴ The required number of times when they toll together is 11.

GIven:

In the 12^th innings, Sachin Tendulkar scores = 120 runs

Formula used:

Average = sum of all numbers/total number

Calculation:

Let Sachin Tendulkar, average scores in 11^th innings be x

Total runs in 11^th innings = 11 × x

⇒ 11x

After increasing the average by 5 runs, new average = x + 5

⇒ (Total runs in 11^th innings + runs in 12^th innings)/12 = x + 5

⇒ (11x + 120)/12 = x + 5

⇒ (11x + 120) = (x + 5) × 12

⇒ 11x + 120 = 12x + 60

⇒ 12x – 11x = 120 – 60

⇒ x = 60

New average = 60 + 5

⇒ 65

∴ The new average is 65.

Shortcut Trick

Actually after scoring 120 runs in 12^th innings the average increased by 5 runs.

then total increased runs = 12 × 5 = 60 runs

Now previous average should be 120 - 60

⇒ 60 runs

New average = 60 + increased average 

⇒ New average = 60 + 5

⇒ 65 runs

∴ The new average is 65.

Given:

The number of revolutions = 1000

And total cover distance = 440 m.

Formula used:

One revolution = total distance covered by wheel/the number of revolutions

Circumference of wheel = 2 × π × r = distance covered by a wheel in one revolution

Diameter of a wheel = 2 × r

Calculation:

Distance in one revolution = 440/1000

⇒ Distance in one revolution = 0.44 m

⇒ 2 × π × r = 0.44

⇒ r = 0.44/(2 × π), where π = 22/7

⇒ r = 0.07 m

Diameter = 2 × 0.07

⇒ Diameter = 0.14 m

∴ The diameter (in meter) of the wheel is 0.14 m.

The logic followed is:-

Carl Lewis, Usain Bolt, Ben Johnson are all sprinters.

Whereas,

Emil Jacktopek is long - distance runner.

Hence, the correct answer is "Emil Jacktopek".

The pattern followed here is:-

7² = 49

Similarly,

17² = 289

Hence, the correct answer is "289".