# SSC CHSL 9th June Shift 1 - QA

**1. SSC CHSL 9th June Shift 1 - QA | Simplification - SSC**

If 2z = x + y, then the value of $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ is:

- A.
0

- B.
1

- C.
2

- D.
5

Answer: Option C

**Explanation** :

Given, 2z = x + y

⇒ z - x = y - z

Now $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ = $\frac{x}{x-\mathrm{z}}$ + $\frac{\mathit{y}}{\mathit{z}\mathit{-}\mathit{x}}$

⇒ $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ = $\frac{x}{x-\mathrm{z}}$ - $\frac{y}{x-z}$

⇒ $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ = $\frac{x-y}{x-\mathrm{z}}$

⇒ $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ = $\frac{x-y}{x-{\displaystyle \frac{(x+y)}{2}}}$ = 2

∴ $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ = 2

**Alternately**,

Assume x = 2 and y = 4, hence z = 3

Now, $\frac{x}{x-\mathrm{z}}$ + $\frac{y}{y-z}$ = $\frac{2}{2-3}$ + $\frac{4}{4-3}$ = -2 + 4 = 2

Hence, option (c).

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**2. SSC CHSL 9th June Shift 1 - QA | Percentage, Profit & Loss - SSC**

A shopkeeper marks his articles at 30% above the cost price and allows the purchaser a discount of 20% for cash buying. What profit per cent does he make?

- A.
4%

- B.
9%

- C.
6%

- D.
5%

Answer: Option A

**Explanation** :

Let the cost price for shopkeeper be Rs. 100

Marked Price = Rs. 130

Selling price after 20% discount = 130 - 26 = 104

∴ Profit % = 4/100 × 100% = 4%.

Hence, option (a).

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**3. SSC CHSL 9th June Shift 1 - QA | Time, Speed & Distance - SSC**

In a trip, Ram can cover a distance of 200 km in 10 hours. First he started by Bike at the speed of 15 km/h. After that his bike broken down and cover the remaining distance by his friend's car at the speed of 25 km/h. Ratio between the distance covered by bike and car is ____________.

- A.
3 : 5

- B.
2 : 3

- C.
1 : 1

- D.
5 : 3

Answer: Option A

**Explanation** :

Let time travelled by bike = t hours, hence time travelled by car = 10 - t hours

Total distance travelled = t × 15 + (10 - t) × 25 = 200

⇒ -10t + 250 = 200

⇒ t = 5 hours.

∴ Distance travelled by bike = 5 × 15 = 75 kms and distance travelled by car = 200 - 75 = 125 kms

Ratio of distance travelled by bike and car = 75 : 125 = 3 : 5

Hence, option (a).

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**4. SSC CHSL 9th June Shift 1 - QA | Simplification - SSC**

If P varies directly as Q, and P = 227 when Q = 232, find P when Q = 116.

- A.
120.5

- B.
113.5

- C.
132

- D.
118

Answer: Option B

**Explanation** :

P varies directly as Q, hence ratio of P and Q will be constant.

∴ 227/232 = P/116

⇒ P = 227/232 × 116 = 113.5

Hence, option (b).

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**5. SSC CHSL 9th June Shift 1 - QA | Simplification - SSC**

If x - y = 25 and xy = 78, then what is the value of x^{2} + y^{2}?

- A.
625

- B.
781

- C.
103

- D.
756

Answer: Option B

**Explanation** :

Given, x - y = 25

Squaring both sides, we get

x^{2} + y^{2} - 2xy = 625

⇒ x^{2} + y^{2} - 156 = 625 [since xy = 78]

⇒ x^{2} + y^{2} = 625 + 156 = 781

Hence, option (b).

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**6. SSC CHSL 9th June Shift 1 - QA | Coordinate Geometry - SSC**

A solid metallic cube of side is $6\sqrt[3]{4}$ cm, is melted and recast into a cuboid of length 12 cm and breadth 9 cm. What is the length (in cm) of the longest diagonal of the cuboid?

- A.
19

- B.
18

- C.
15

- D.
17

Answer: Option D

**Explanation** :

Side of the cube $6\sqrt[3]{4}$

Volume of the cube = ${\left(6\sqrt[3]{4}\right)}^{3}$ = 864

Volume of the cuboid = 12 × 9 × height = 864

⇒ height = 8

Longest diagonal of the cuboid is the body diagonal

∴ Longest diagonal = $\sqrt{{12}^{2}+{9}^{2}+{8}^{2}}$ = 17

Hence, option (d).

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**7. SSC CHSL 9th June Shift 1 - QA | Ratio, Proportion & Variation - SSC**

In a 1200 m race, the ratio of the speeds of two contestants Meenal and Nitu is 5:7. If Meenal has a start of 500 m,then Meenal wins by:

- A.
220 m

- B.
240 m

- C.
250 m

- D.
225 m

Answer: Option A

**Explanation** :

Meenal get a start of 500 meters, hence Meena has to run for 1200 - 500 = 700 meters.

Since the ratio of speeds of Meenal and Nitu is 5 : 7, by the time Meenal travels 700 meters, Nitu will travel 700 × 7/5 = 980 meters.

∴ Nitu will be 1200 - 980 = 220 meters behind Meenal.

Hence, option (a).

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**8. SSC CHSL 9th June Shift 1 - QA | Percentage, Profit & Loss - SSC**

The tax on a commodity diminishes by 14% and its consumption increases by 10%. Find the effect on revenue.

- A.
Decreases by 9.5%

- B.
Decreases by 6.5%

- C.
Decreases by 5.4%

- D.
Decreases by 7.4%

Answer: Option C

**Explanation** :

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**9. SSC CHSL 9th June Shift 1 - QA | Tables & Graphs - SSC**

The following pie chart shows the different coloured dresses worn by 60 students in a college party. Study the pie chart and answer the question that follows.

The number of students who wore cement-coloured dress (sector which represents 20%) is:

- A.
20

- B.
10

- C.
6

- D.
12

Answer: Option D

**Explanation** :

Number of students who wore cement-coloured dress = 20% of 60 = 20/100 × 60 = 12.

Hence, option (d).

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**10. SSC CHSL 9th June Shift 1 - QA | Trigonometry - SSC**

If $\mathrm{cos}e{c}^{2}\theta $ + $co{t}^{2}\theta $ = $\frac{1}{3},$ Where 0 ≤ θ ≤ $\frac{\pi}{2},$ then the value of $\mathrm{cos}e{c}^{4}\theta $ - $co{t}^{4}\theta $ is:

- A.
$\frac{2}{3}$

- B.
$-\frac{1}{3}$

- C.
$\frac{1}{3}$

- D.
$-\frac{2}{3}$

Answer: Option C

**Explanation** :

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**11. SSC CHSL 9th June Shift 1 - QA | Circles - SSC**

Find the total surface area of a solid hemisphere whose radius is 4.2 cm.

(Take π = 22/7)

- A.
266.32 cm

^{2} - B.
366.32 cm

^{2} - C.
166.32 cm

^{2} - D.
466.32 cm

^{2}

Answer: Option C

**Explanation** :

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**12. SSC CHSL 9th June Shift 1 - QA | Percentage, Profit & Loss - SSC**

40% of Ranita’s income is equal to 56% of Bhaskar’s income. If Ranita’s income was ₹800 more than what it is and Bhaskar’s income was ₹ 2,000 more than what it is, then the ratio of the incomes of Ranita and Bhaskar would have been 4 : 3. What is the actual combined income of Ranita and Bhaskar?

- A.
₹67,200

- B.
₹68,200

- C.
₹66,800

- D.
₹67,800

Answer: Option A

**Explanation** :

Let Ranita's income be R and that of Bhaskar be B.

Given, 40% of R = 56% of B

⇒ 0.4R = 0.56B

⇒ R : B = 0.56 : 0.4 = 56 : 40 = 7 : 5

∴ R = 7x and B = 5x

Now, given:

(R + 800) : (B + 2000) = 4 : 3

⇒ 3(7x + 800) = 4(5x + 2000)

⇒ 21x + 2400 = 20x + 8000

⇒ x = 5600

∴ Combined income of R and B = 7x + 5x = 12x = 12 × 5600 = Rs. 67,200

Hence, option (a).

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**13. SSC CHSL 9th June Shift 1 - QA | Average, Mixture & Alligation - SSC**

Two grandparents, two parents, and three grandchildren make up a family. The average present age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years.What is the present age of the family (in years)?

- A.
$33\frac{4}{9}$

- B.
$31\frac{5}{7}$

- C.
$27\frac{3}{7}$

- D.
$34\frac{2}{5}$

Answer: Option B

**Explanation** :

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**14. SSC CHSL 9th June Shift 1 - QA | Average, Mixture & Alligation - SSC**

The average weight of 18 persons increases by 2.5 kg when a new person comes in place of one of them weighing 72 kg. The weight of the new person is:

- A.
107 kg

- B.
127 kg

- C.
117 kg

- D.
77 kg

Answer: Option C

**Explanation** :

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**15. SSC CHSL 9th June Shift 1 - QA | Time & Work - SSC**

If 15 people take 5 days to complete a job, in how many days can 25 people finish that work?

- A.
2

- B.
4

- C.
3

- D.
1

Answer: Option C

**Explanation** :

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**16. SSC CHSL 9th June Shift 1 - QA | Coordinate Geometry - SSC**

If the curved surface area of a closed cylinder is 225 cm^{2} and the area of its base is 169 cm^{2}, then find the total surface area of the cylinder.

- A.
394 cm

^{2} - B.
343 cm

^{2} - C.
563 cm

^{2} - D.
195 cm

^{2}

Answer: Option C

**Explanation** :

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**17. SSC CHSL 9th June Shift 1 - QA | Simplification - SSC**

Simplify the following expression.

4 ÷ [ 2 + 2 ÷ {2 + 2 ÷ (2 + $\frac{2}{3}$)}]

- A.
$\frac{11}{15}$

- B.
$-\frac{11}{15}$

- C.
$\frac{22}{15}$

- D.
$-\frac{22}{15}$

Answer: Option C

**Explanation** :

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**18. SSC CHSL 9th June Shift 1 - QA | Simplification - SSC**

If (ab + bc + ca) = 0, then what is the value of ($\frac{1}{{a}^{2}-bc}$ + $\frac{1}{{b}^{2}-ca}$ + $\frac{1}{{c}^{2}-ab}$)?

- A.
2

- B.
0

- C.
1

- D.
a + b + c

Answer: Option B

**Explanation** :

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**19. SSC CHSL 9th June Shift 1 - QA | Tables & Graphs - SSC**

The following pie chart shows the spending of a country on tourism in various districts during a particular year. Total spending of the country = ₹ 15,62,000.

Study the pie chart and answer the following question.

The amount spent on districts D and E exceeds that on district A and F by (in ₹):

- A.
20

- B.
10

- C.
6

- D.
1,56,200

Answer: Option D

**Explanation** :

The amount spent on districts D and E exceeds that on district A and F by (18% + 16% - 12% - 12%) of Rs. 15,62,000

= 10% of 15,62,000

= Rs. 1,56,200

Hence, option (d).

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**20. SSC CHSL 9th June Shift 1 - QA | Tables & Graphs - SSC**

The table below gives information regarding the number of attempts made and number of successful attempts by six candidates in the gate examination.

The number of times Rajesh took the exam was 30% less than the number of times dinesh took it.

What is the approximately percentage of times that dinesh cleared the exam out the times that he attempted it?

- A.
34.01%

- B.
31.23%

- C.
35.71%

- D.
32.71%

Answer: Option C

**Explanation** :

Number of attempts made by Rajesh is 20 × 0.7 = 14

∴ Required percentage = 5/14 × 100% = 35/71%

Hence, option (c).

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**21. SSC CHSL 9th June Shift 1 - QA | Percentage, Profit & Loss - SSC**

A sells a car to B at a gain of 10% and B again sells it to C at a profit of 5%. If C pays ₹4,06,000 to B, what is the cost price of the car for A?

(Consider integral part only)

- A.
₹3,50,000

- B.
₹3,68,950

- C.
₹3,51,515

- D.
₹4,51,515

Answer: Option C

**Explanation** :

B sells the car for Rs. 4,06,000 at 5% profit.

B's cost price = 4,06,000/1.05

A sells the car for Rs. 4,06,000/1.05 at 10% profit.

A's cost price = 4,06,000/(1.05 × 1.1) = Rs. 3,51,515

Hence, option (c).

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**22. SSC CHSL 9th June Shift 1 - QA | Coordinate Geometry - SSC**

In the following figure, ∆ABC is an inscribed triangle as shown and DE is an tangent to the circle at C. If m∠ACD = 65° and m∠ACB = 35°, find the measure of m∠BAC

- A.
80°

- B.
75°

- C.
60°

- D.
65°

Answer: Option A

**Explanation** :

In the given circle, m∠ACD = m∠ABC = 65°

[Anglel made by tangent and a chord is same as angle subtended by same chord in opposite segment of the circle.]

In ∆ABC,

∠ABC + ∠BCA + ∠CAB = 180°

∴ 65° + 35° + ∠CAB = 180°

⇒ ∠CAB = 80°

Hence, option (a).

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**23. SSC CHSL 9th June Shift 1 - QA | Percentage, Profit & Loss - SSC**

One dozen books quoted at ₹120 are available at 15% discount. How many books can be bought for ₹51?

- A.
8

- B.
5

- C.
6

- D.
7

Answer: Option C

**Explanation** :

12 books are available for Rs. 120 × 0.85 = Rs. 102.

∴ Number of books that can be bought for Rs. 51 = 6.

Hence, option (c).

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**24. SSC CHSL 9th June Shift 1 - QA | Simple & Compound Interest - SSC**

Find the compound interest on ₹35,000 in 2 years at 6% per annum, the interest being compounded half-yearly (nearest to a ₹):

- A.
₹4,000

- B.
₹4,193

- C.
₹4,393

- D.
₹4,388

Answer: Option C

**Explanation** :

Amount due after 2 years = 35000${\left(1+\frac{6/2}{100}\right)}^{2\times 2}$ = Rs. 39,393.

∴ Interest = 39,393 - 35,000 = Rs. 4,393.

Hence, option (c).

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**25. SSC CHSL 9th June Shift 1 - QA | Simplification - SSC**

Which of the following options is NOT divisible by 18?

- A.
571032

- B.
732546

- C.
245798

- D.
459018

Answer: Option C

**Explanation** :

Option (c): 245798 is not divisible by 3 hence it will not be divisible by 18 also.

Hence, option (c).

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