## Simplification Questions - 1

Simplify: 32 Ã· 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 Ã· 8 $\displaystyle \times$ 24 + 16 => 4 $\displaystyle \times$ 24 + 16 = 96 + 16 = 112.

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

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

Workspace
Simplify: 2 + 3 $\displaystyle \times$ [ 3 $\displaystyle \times$ 4 Ã· 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 â€“ $\displaystyle \frac{8}{5}$ of 60 + ? = 12
• 48
• 24
• 56
• 63
• 14
Explanation

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

45 â€“ 96 + ? = 12 => 96 + 12 = 108 â€“ 45 = 63

[63 + 45 = 108 â€“ 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 = $\displaystyle x \ â€“ \ \frac{1}{3}$ $\displaystyle x \ = \ \frac{2}{3} x$

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 = $\displaystyle \frac{4}{5}$ â€“ $\displaystyle \frac{4}{25}$ = $\displaystyle \frac{16}{25}$

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

Remaining = $\displaystyle \frac{16}{25}$ â€“ $\displaystyle \frac{2}{25}$ = $\displaystyle \frac{14}{25}$

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

Water = 1 â€“ $\displaystyle \frac{14}{25}$ = $\displaystyle \frac{11}{25}$ 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 â€“ 16 = 64

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

Remaining milk = 64 â€“ 8 = 56 lr

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

Workspace
x Ã· 4 $\displaystyle \times$ 5 + 10 â€“ 12 = 48, then x = ?
• 60
• 40
• 100
• 28
• 50
Explanation

48 + 12 = 60 â€“ 10 = 50 Ã· 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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