The Correct answer is option 1 i.e. 125.

When divided by 7, it leaves the remainder 1

So the dividend = 7k + 1

 This number is the quotient when divided by 5 and leaves the remainder 1

So the dividend = 5 × (7k + 1) + 1

⇒ 35k + 6

This number is the quotient when divided by 3 and leaves the remainder 2

So the dividend = 3 × (35k + 6) + 2

⇒ 105k + 20

For the least possible number, k = 1

105 × 1 + 20 = 125

The correct answer is Option 2 i.e. 5.33 hours.

Efficiency is inversely proportional to the time taken.

25% = 1/4 and 25% more means the ratio will be 2 : 2.5

The ratio of efficiency of A to B = 4 : 5

The ratio of time taken = 5 : 4

Time taken by A = 12 hours

5 unit = 12 hours

4 unit = 48/5 hours

A can do the work in 12 hours, and B in 48/5 hours.

Together they can do in = 1/(1/12 + 5/48) = 48/9 = 5.33 hours

The correct answer is option 1 i.e. 2 : 5

Given:

Bus A's speed : Bus B's speed = 5 : 3

Distance travelled by bus A = 200 km

Distance travelled by bus B = 300 km 

Formula used :

Time = Distance/speed ----- (1)

Calculations :

Let the ratio of their speed be 5x and 3x

Ratio of time take by Bus A and Bus B 

Using equation (1)

⇒ (200/5x) : (300/3x)

⇒ 40 : 100

⇒ 2 : 5

The correct answer is Option 1 i.e. 32.

Let a, b and c are first, second and third numbers respectively.

Sum of first two numbers = a + b = 2 × 20 = 40

Sum of last two numbers = b + c = 2 × 36 = 72

Required difference = b + c - (a + b) = c - a = 72 - 40 = 32

The correct answer is Option 1 i.e. Rs. 26320.

Amount invested by A = Rs 12000

Amount invested by B = Rs 15000

Amount invested by C = Rs 18000

Total profit after 2 years = Rs. 84600

Total amount = amount invested × number of months

Total amount invested by A = 12000 × 24 = 288000

Total amount invested by B = 15000 × 18 = 270000

Total amount invested by C = 18000 × 14 = 252000

The ratio of their investment i.e. A : B : C = 288000 : 270000 : 252000 = 16 : 15 : 14

C's share in profit = (14/45) × 84600 = Rs. 26320

The correct answer is option 2 i.e. 9%.

S.I. = (P × R × T)/100

Let, the rate be R%

Now, according to the question-

⇒ 2925 = (1500 × R × 5)/100 + (1800 × R × 3)/100 + (2800 × R × 7)/100

⇒ 2925 = (7500 × R)/100 + (5400 × R)/100 + (19600 × R)/100

⇒ 2925 =  75R + 54R + 196R

⇒ 2925 = 325R

⇒ R = 9%

The correct answer is option 3 i.e. 404.25 cm³

If a semi-circular shape is bent into a conical shape, then the radius of the semi-circle is equal to the slant height of the cone. and the length of the circumference of the semi-circle is equal to the perimeter of the base of the cone. 

The volume of the cone = (1/3)πr²h

The slant height of the cone = 7√3 cm

Let the radius of the cone = R cm

The circumference of the semi-circle = the perimeter of the base of the cone

π(7√3) = 2πR

R = (7√3)/2

Using Pythagoras' theorem in the right-angle triangle in cone, 

(Perpendicular height)² = ( slant height)² - (radius)² 

= ( 7√3)² - ( 7√3/2)²

= 147 - 147/4

= 147 × 3/4 = 441/4

Perpendicular height = 21/2

The volume of the cone

= (1/3)(22/7)( 7√3/2)²(21/2) = 404.25 cm³.

The correct answer is option 4 i.e. 4 : 7

Given,

Cost price of the desired mixture = 115 ÷ 1.25 = Rs. 92

To determine the required ratio of mixing, we use alligation rule,

So, ratio of quantities of basmati rice and Samba rice to be mixed = 8 : 14

= 4 : 7

The correct answer is option 4 i.e. 70.

The original number of items = remaining items × (100)/(remaining percent)

The remaining percent of watermelons = (100% - 60%) = 40%

The initial number of watermelons = 28 × 100/40 = 70

The correct answer is option 2 i.e. 19/36.

Calculations:

⇒ [(34/12 + 11/16 - 12.5 ÷ 480/120 )(13/6 - 17/18)] × 12/11

⇒ [(17/6 + 11/16 - 125/10 × 120/480)(13/6 - 17/18)] × 12/11

⇒ [(17/6 + 11/16 - 125/10 × 120/480)(13/6 - 17/18)] × 12/11

⇒ [(17/6 + 11/16 - 25/8){(39 - 17)/18}] × 12/11

⇒ [{(136 + 33 - 150)/48}{22/18}] × 12/11

⇒ [{19/48}{22/18}] × 12/11

⇒ [{19/48}{11/9}] × 12/11

⇒ (209/432) × (12/11)

⇒ (209/432) × (12/11)

⇒ 19/36