Tag: ways to multiply and divide

Place value of a digit increases by $10$ times as it moves from right to left.

156 $\times$ 0 = 0

The resultant product of $3$ negative signs would be negative.

$
-{ \frac { 1 }{ 4 }  }^{ -3 }{ \times \frac { 1 }{ 4 }  }^{ 4 }\div { 4 }^{ -2 }{ \quad =\quad -4 }^{ (10x+1) }\ \ -{ 4 }^{ 3 }{ \times 4 }^{ -4 }\times { 4 }^{ 2 }{ \quad =\quad -4 }^{ (10x+1) }\ { -4 }^{ 3-4+2 }{ \quad =\quad -4 }^{ (10x+1) }\ { -4 }^{ 1 }{ \quad =\quad -4 }^{ (10x+1) }\ 1\quad =\quad 10x\quad +1\ 10x\quad =\quad 0\ x\quad =\quad 0
$

Total age of 6 family members four year ago =$25\times 6=150$years
Total age of 6 family member now=150+$4\times 6=150+24=174$years
Total age of 6 family member and child =$25\times 7=175$year
Age of child =175-174=1 year

45 % of 1500 + 35 % of 1700 = ? % of 3175
Or $\frac{45}{100}\times 1500+\frac{35}{100}\times 1700= \frac{x}{100}\times 3175$
Let x is new %

Or $45\times 1500+35\times 1700=3175\times x$
OR 67500+59500=3175x
Or x=$\frac{127000}{3175}=40%$

$(100 + 2) \times (100 + 3)$
           [Using $(x +a) (x+b)=x^2+(a+b)x+ ab$]
$ = (100)^2 + (2 + 3) \times 100 + 2 \times 3$
$ = 10000 + 5 \times 100 + 6 = 10000 + 500 + 6 = 10506$

Let the number of pineapple and watermelon be x and y
Then 7x+5y=38 (given cost of pineapple and watermelon is Rs 7and Rs 5
Or 5y=38-7x
Or $y=\frac{38-7x}{5}$ 
clearly y is whole number only when (38-7x) is divisible by 5
This happens when x=4

Putting x=2, we get $2^2\left(2^2-1\right)= 12. So, x^2\left(x^2-1\right)$ is always divisible by 12

Suresh travelled 1200 km by air which form (2/5) of his trip. 
Then total distance of journey=$\frac{5}{2}\times 1200=3000 km$
Suresh travelled $\frac{1}{3}$of journey by car =$\frac{1}{3}\times 3000=1000 km$
Then suresh travelled distance by train =3000-1200-1000=800 km
If whole journey by train in 8 hours 
So speed of train=$\frac{3000}{8}$=375 km/Hr