Simplification Problems for SSC CGL

1.

853 + ? ÷ 17 = 1000

   A.) 2499
   B.) 2566
   C.) 2965
   D.) 2864

Answer: Option 'A'

853 + ?/17 = 1000
?/17 = 1000 – 853 = 147
? = 17 × 147 = 2499

2.

65% of 400 + √? = 44% of 800 – 12% of 400

   A.) 1936
   B.) 2054
   C.) 1635
   D.) 1954

Answer: Option 'A'

65% of 400 + √? = 44% of 800 – 12% of 400
65% of 400 + √? = 44% of 800 – 12% of 400
⇒ (50% of 400 + 10% of 400 + 5% of 400) + √? = (50% of 800 – 6% of 800) – 12% of 400
⇒ (200 + 40 + 20) + √? = (400 – 48) – 48
or, √? = 352 – 48 – 260 = 44
∴ ? = (44)2 = 1936.65% of 400 + √? = 44% of 800 – 12% of 400
⇒ (50% of 400 + 10% of 400 + 5% of 400) + √? = (50% of 800 – 6% of 800) – 12% of 400
⇒ (200 + 40 + 20) + √? = (400 – 48) – 48
or, √? = 352 – 48 – 260 = 44
∴ ? = (44)2 = 1936.

3.

(14896 ÷ 19) ÷ 16 = ?

   A.) 59
   B.) 69
   C.) 49
   D.) 38

Answer: Option 'C'

(14896 ÷ 19) ÷ 16 = ?
⇒ ? = 14896/19 ÷ 16
⇒ ? = 14896/19 ÷ 16  ⇒  784/16 = 49

4.

6156  ÷ √? × 53 = 4028

   A.) 6889
   B.) 6561
   C.) 6995
   D.) 6235

Answer: Option 'B'

6153 × 53/√? = 4028
⇒ √? = 80.96 ≈ 81
⇒ ? = 6561

5.

8195 ÷ 745 + ? × 12 = 7847

   A.) 657
   B.) 653
   C.) 601
   D.) 596

Answer: Option 'B'

8195 ÷ 745 + ? × 12 = 7847
or,  ? × 12 = 7847 – 8195/745 = 7847 – 11
or,   ? × 12 = 7836
∴    ? = 653.

6.

98643 – 21748 = 51212 + ?

   A.) 25683
   B.) 26687
   C.) 27893
   D.) 26874

Answer: Option 'A'

Given eqn,
98643 – 21748 = 51212 + ? 
⇒ ? = 98643 – 21748 – 51212 
⇒ ? = 25683

7.

A contractor pays Rs. 20 to a worker for each day and the worker forfeits Rs. 10 for each day if he is idle. At the end of 60 days, the worker gets Rs. 300. Find for how many days the worker was idle?

   A.) 34 days
   B.) 30 days 
   C.) 28 days
   D.) 40 days

Answer: Option 'B'

Step 1: Number of days worked by the worker = 60 and he remained idle for x days. Therefore, number of days worked = (60 – x) 
Step 2: Each day he was getting paid Rs. 20. Therefore, the payment received for working days = (60 – x) 20
Step 3: After subtracting the amount which he forfeited, he receives Rs. 300. 
Therefore,
(60 – x) 20 – 10x = 300
1200 – 20x – 10x = 300 
900 = 30x 
x = 30 days

8.

70% of 1680 + ?% of 1750 = 55% of 2820 – 886

   A.) –29.2
   B.) 30
   C.) 34
   D.) 54

Answer: Option 'A'

70% of 1680 + ?% of 1750 = 55% of 2820 – 886
70/100 × 1680 + ?/100 × 1750 = 55/100 × 2820 – 886
1176 + ?/10 × 175 = 1551 – 886 = 665
?/10 × 175 = 665 – 1176 = –511
? = (–511 × 10)/175 = –29.2

9.

46% of 1250 + ?% of 4680 = 1183.4

   A.) 18
   B.) 24
   C.) 27
   D.) 13

Answer: Option 'D'

46% of 1250 + ?% of 4680 = 1183.4
46/100 × 1250 + ?/100 × 4680 = 1183.4
575 + ?/5 × 234 = 1183.4
?/5 × 234 = 1183.4 – 575 = 608.4
? = (608.4 × 5)/234 = 3042/234  = 13

10.

If x/y = 3/4 and 8x + 5y = 22, then find the value of x.

   A.) 1.5
   B.) 2.3
   C.) 4.5
   D.) 3.6

Answer: Option 'A'

y = 4/3 x
Substitute this value in 8x+5y=22
8x + 5(4/3) x = 22
44x=66
x=1.5

11.

(764 × ?) ÷ 250 = 382

   A.) 115
   B.) 125
   C.) 135
   D.) 145

Answer: Option 'B'

(764 × ?)/250 = 382
? = (382 × 250)/764 = 125

12.

Simplify: 13.05 × 4.5 ÷ 0.5

   A.) 119.75
   B.) 117.45 
   C.) 115.50
   D.) 140.60 

Answer: Option 'B'

Follow the rule of ‘VBODMAS’ 
No bar, No bracket. Hence, first step starts from ‘DMAS’ 
Step 1: Divide 4.5 ÷ 0.5=9
Step 2: Multiply 13.05 × 9 = 117.45

13.

1035 ÷ [(3/4) of (71 + 65) – 15 ¾] = ?

   A.) 12
   B.) 16
   C.) 17
   D.) 20

Answer: Option 'A'

1035 ÷ [(3/4)× 136 – 63/4] = x
X = 1035 ÷ [102 – (63/4)]
X = 1035 ÷ [(408 – 63)/4]
X = 1035 ÷ (345/4)
X = 1035 × 4/345
X = 12

14.

4/9 × 1701 + 2/11 × 1386 = ?

   A.) 180
   B.) 1008
   C.) 1080
   D.) 1800

Answer: Option 'B'

4/9 × 1701 + 2/11 × 1386 = ?
? = (4 × 189) + (2 × 126)
? = 756 + 252 = 1008.
Hence, option B is correct.

15.

[(4)3 × (5)4] ÷ (4)5 = ?

   A.) 39.0625
   B.) 44.0625
   C.) 43.0625
   D.) 41.0625

Answer: Option 'A'

? = [43 × 54]/45 = 54/42 = 625/16 = 39.0625

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