Simplification Questions - 1

Simplify: 32 ÷ 8 $\displaystyle \times $ 24 + 16 =
  • 130
  • 124
  • 120
  • 115
  • 112
Explanation   

Follow BODMAS rule, Bars, remove brackets in (), {},[] order, Of, Division, Multiplication, Addition, Subtraction respectively.

32 ÷ 8 $\displaystyle \times$ 24 + 16 => 4 $\displaystyle \times$ 24 + 16 = 96 + 16 = 112.

Workspace
Simplify: 65 x 65 ÷ 13 + [ 4 + 18 ÷ 3]
  • 330
  • 335
  • 256
  • 345
  • 375
Explanation   

65 X 65 ÷ 13 + [ 4 + 18 ÷ 3] => 65 X 65 ÷13 +[ 4 + 6] => 65 X 5 + 20 = 325 + 10 = 335

Workspace
Simplify: 2 + 3 $\displaystyle \times$ [ 3 $\displaystyle \times$ 4 ÷ 2 $\displaystyle \times$ $\displaystyle \frac{1}{2}$ ]
  • 12
  • 13
  • 14
  • 11
  • 16
Explanation   
2 + 3 [3] => 2 + 9 = 11
Workspace
Simplify $\displaystyle \frac{3}{4} $ of 60 – $\displaystyle \frac{8}{5}$ of 60 + ? = 12
  • 48
  • 24
  • 56
  • 63
  • 14
Explanation   

60 $\displaystyle \times \frac{3}{4}$ = 45, 60 $\displaystyle \times \frac{8}{5}$ = 96

45 – 96 + ? = 12 => 96 + 12 = 108 – 45 = 63

[63 + 45 = 108 – 96 = 12]

Workspace
A farmer divided certain number of acres of land among 3 sons and 1 daughter in such a way that $\displaystyle \frac{1}{3}$rd of the total land was given to elder son, $\displaystyle \frac{1}{2}$ of the remaining was given to second son, $\displaystyle \frac{1}{3}$rd of the remaining was given to his younger son, and the remaining to his daughter. As a result, the younger son and daughter received equal number of acres. Find the total number of acres divided, if daughter gets 12 acres land.
  • 72
  • 90
  • 120
  • 84
  • 62
Explanation   

Let total number of land x acre

Elder son = $\displaystyle x \times \frac{1}{3}$ = $\displaystyle \frac{1}{3}x$

Remaining = $\displaystyle x \ – \ \frac{1}{3}$ $\displaystyle x \ = \ \frac{2}{3} x $

Second son = $\displaystyle \frac{1}{2}$ of $\displaystyle \frac{2}{3} x $ = $\displaystyle \frac{1}{3} x$

Remaining = $\displaystyle \frac{1}{3} x$ = 24 acre [12 + 12 = 24, younger son + Daughter]

$\displaystyle \frac{1}{3} x$ = 24, then x = 24 $\displaystyle \times \frac{3}{1}$ = 72

Workspace
A container is filled with milk and water, milk contains $\displaystyle \frac{4}{5}$ th part of the container, $\displaystyle \frac{1}{5}$ th and $\displaystyle \frac{1}{8}$ th part of the solution successively replaced by water, then what part of the container, water contains ?
  • $\displaystyle \frac{14}{25}$
  • $\displaystyle \frac{16}{25}$
  • $\displaystyle \frac{3}{5}$
  • $\displaystyle \frac{7}{10}$
  • $\displaystyle \frac{11}{25}$
Explanation   

Quantity of milk : water = $\displaystyle \frac{4}{5}$ : $\displaystyle \frac{1}{5}$

First replacement = $\displaystyle \frac{1}{5}$ of $\displaystyle \frac{4}{5}$ = $\displaystyle \frac{4}{25}$

Remaining milk = $\displaystyle \frac{4}{5}$ – $\displaystyle \frac{4}{25}$ = $\displaystyle \frac{16}{25}$

2nd replacement = $\displaystyle \frac{1}{8}$ th of $\displaystyle \frac{16}{25}$ = $\displaystyle \frac{16}{200}$ or $\displaystyle \frac{2}{25}$

Remaining = $\displaystyle \frac{16}{25}$ – $\displaystyle \frac{2}{25}$ = $\displaystyle \frac{14}{25}$

Quantity of milk = $\displaystyle \frac{14}{25}$

Water = 1 – $\displaystyle \frac{14}{25}$ = $\displaystyle \frac{11}{25}$ th part

[Or]

Let the container contains 100 lr of milk and water

Then milk = $\displaystyle \frac{4}{5}$ = 80lr

1st repl = $\displaystyle \frac{1}{5}$ th of 80 = 16 lr

Remaining = 80 – 16 = 64

2nd repl = $\displaystyle \frac{1}{8}$ th of 64 = 8 lr

Remaining milk = 64 – 8 = 56 lr

Water = 100 – 56 = 44 lr, if expressed in a fraction $\displaystyle \frac{44}{100}$ = $\displaystyle \frac{11}{25}$

Workspace
x ÷ 4 $\displaystyle \times$ 5 + 10 – 12 = 48, then x = ?
  • 60
  • 40
  • 100
  • 28
  • 50
Explanation   

Follow reverse process

48 + 12 = 60 – 10 = 50 ÷ 5 = 10 $\displaystyle \times$ 4 = 40

Workspace
A boy had a certain number of marbles. 1st day he lost $\displaystyle \frac{1}{5}$th of the marbles. From the remaining marbles, he lost $\displaystyle \frac{1}{4}$th on the 2nd day. On the 3rd day, he lost $\displaystyle \frac{1}{2}$ of the marbles that were left. On 4th day he gained $\displaystyle \frac{1}{3}$rd of the marbles that he had. Now, the boy has 20 marbles. How many marbles were there in the beginning ?
  • 30
  • 45
  • 24
  • 36
  • 20
Explanation   

Number of marbles on 4th day = 20

4th = 20 = 1 $\displaystyle \frac{1}{3}$ = $\displaystyle \frac{4}{3}$ = 20 => 20 $\displaystyle \times \frac{3}{4}$ = 15

3rd = $\displaystyle \frac{1}{2}$ = 15 = 15 $\displaystyle \times \frac{2}{1}$ = 30

2nd = 30 = 1 + $\displaystyle \frac{1}{4}$ = 30 = $\displaystyle \frac{5}{4}$ = $\displaystyle \frac{4}{5} \times $ 30 = 24

1st day = 1 - $\displaystyle \frac{1}{5}$ = $\displaystyle \frac{4}{5}$ = 24 = 24 $\displaystyle \times \frac{5}{4}$ = 30

In the beginning he had 30 marbles

Workspace
Certain number of worms are placed in a container. The number of worms increases by three times every day and the container is completely filled with worms in 12 days. On what day, the worms were $\displaystyle \frac{1}{3}$rd of the container ?
  • 9 days
  • 3 days
  • 4 days
  • 11 days
  • 14 days
Explanation   

As every day the worms increases by 3 times

$\displaystyle \frac{1}{3} \ \times $ 3 = 1 [full]

Therefore on 11th day

Workspace
Speed of a car doubles after every hour. After travelling for 3 hours, the speed of the car is now 160km/hr. What is the total distance travelled by the car ?
  • 300 km
  • 160 km
  • 140 km
  • 240 km
  • 280 km
Explanation   

160 is actually in 4th hour

We have to calculate for the first 3 hrs

On third hour $\displaystyle \frac{160}{2}$ = 80 km/h

Second hr $\displaystyle \frac{80}{2}$ = 40km/hr

First hour $\displaystyle \frac{40}{2}$ = 20km/hr

Total distance covered = 80 + 40 + 20 = 140 km

Workspace

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