Explanation

To find the greatest number that exactly divides 145, 360, and 578, we need to find their greatest common divisor (GCD or HCF).

Let's find the factors:

145 = 5 × 29

360 = 2^3 × 3^2 × 5

578 = 2 × 17 × 17

The only common factor is 1.

Explanation

Meat:

Chicken = 4/6 = 2/3 kg

Mutton = 2/3 kg

Beef = 5/12 kg

Total meat weight = 2/3 + 2/3 + 5/12

= (8 + 8 + 5)/12

= 21/12

= 7/4 kg

Grocery:

Sugar = 2 × 4/3 = 8/3 kg

Rice = 3 × 3/4 = 9/4 kg

Total grocery weight = 8/3 + 9/4

= (32 + 27)/12

= 59/12 kg

Total weight = Meat weight + Grocery weight

= 7/4 + 59/12

= (21 + 59)/12

= 80/12

= 20/3 kg

Explanation

To find 60 percent of 100, use the formula:

$$text{Percentage of a number} = left(frac{text{Percent}}{100}right) times text{Number}$$ $$= left(frac{60}{100}right) times 100 = 0.6 times 100 = 60$$

Explanation

Given:
Cost Price (CP) = Rs. 60,000
Selling Price (SP) = Rs. 66,000

Profit (P):
$$

$P=SP-CP$

$=66,000-60,000=Rs.6,000$

Profit %:

$$text{Profit$$

Conclusion:
Ali’s profit percentage is 10%. ✅

Explanation

To find the area of the carpeting part, we need to find the area of the inner rectangle (without carpet) and subtract it from the total area.

Length of inner rectangle = 7.8 - 22.3 = 3.2 m

Width of inner rectangle = 6.5 - 22.3 = 1.9 m

Area of the room = 7.8 * 6.5 = 50.7 m^2

Area of inner rectangle = 3.2 * 1.9 = 6.08 m^2

Area of carpet = Total area - Inner area

= 50.7 - 6.08

= 44.62 m^2

Explanation

To find when all three tests will be conducted together again, we need to find the least common multiple (LCM) of 3, 6, and 9.

The LCM of 3, 6, and 9 is 18.

So, all three tests will be conducted together again after:

18 days

Explanation

Khadija is thrice as old as her daughter, so:

K = 3D

The sum of their ages is 45:

K + D = 45

3D + D = 45

4D = 45

D = 45/4

D = 11.25 (12)

Explanation

Perimeter formula for a rectangle: 2 × (Length + Width)

2 × (210 + 118) = 2 × 328 = 656 cm

Explanation

Digit 7 appears in both units and tens places.

Total count = 9 (units) + 9 (tens) + 1 (double 7 in 77)

= 19 + 1

= 20 times.

Explanation

The largest 4-digit number is 9999.

Dividing 9999 by 88 gives: 9999 ÷ 88 = 113.625 → Integer part = 113

113 × 88 = 9944, which is the largest 4-digit number divisible by 88.