30. SSC CGL 2023 

Exam Date 25/07/2023 

Exam Time 11:45 AM - 12:45 PM 

Section : Quantitative Aptitude

Q.1 If RP and RQ are two tangents to a circle with centre O such that ∠POQ = 120°, where P and Q are the points on the circle and R is a point outside the circle then ∠PRQ is equal to: 

1. 90° 

2. 45° 

3. 75° 

4. 60° 

Q.2 A can do $\frac{1}{3}$ of a piece of work in 32 days. B can do $37\frac{1}{2}%$ of the same work in 24 days. while C can do 60% of the same work in 48 days. B and C together started and worked for x days. After x days, B left the work and Ajoincd C and both completed the remaining work in (x + 8) days. If the ratio of the work done by (B + C) together to the work done by (A + C) together is 9 : 11. then what fraction of the same work can be completed by C alone in 3.5); days? 

1. $\frac{7}{10}$ 

2. $\frac{3}{4}$ 

3. $\frac{4}{5}$ 

4. $\frac{18}{25}$

Q.3 ₹8,500 becomes ₹11,050 in 6 years at a certain rate of simple interest. If the rate becomes 1.8 times of itself, the amount of the same principal in 5 years will be: 

1. ₹15,625 

2. ₹14,350 

3. ₹13,550 

4. ₹12,325 

Q.4 The value of which of the following is different from the other options? 

1. sec 60° 

2. sin 90° 

3. cos 0° 

4. tan 45° 

Q.5 Find the value of tan (−1125°). 

1. 1 

2. –1 

3. 0 

4. $\frac{1}{2}$ 

Q.6 P and Q together complete a job in $4\frac{2}{5}$ days. R and S complete the same job in $4\frac{8}{9}$ days. If P, Q, R and S work together, how many days do they need to complete the same job? 

1. $1\frac{7}{18}$ 

2. $2\frac{7}{18}$ 

3. $1\frac{6}{19}$ 

4. $2\frac{6}{19}$ 

Q.7 Simplify$\frac{256{{x}^{4}}-16{{y}^{4}}}{\left( 80{{x}^{2}}-20{{y}^{2}} \right)\left( 16{{x}^{2}}+4{{y}^{2}} \right)}$. 

1. $\frac{1}{20}$ 

2. $\frac{1}{5}$ 

3. 5 

4. $\frac{2}{5}$ 

Q.8 Which of the following numbers is divisible by 99? 

1. 44775 

2. 31548 

3. 60687 

4. 84456 

Q.9 A can finish a work in 60 days. He works at it for 15 days and then B alone finishes the remaining work in 48 days. In how much time can A and B working together finish the work? 

1. $\frac{171}{37}$ days 

2. $\frac{960}{31}$ days 

3. 45 days 

4. 51 days 

Q.10 A family income is ₹35,000 in a month. The family spends the income on various expenditures, viz., food, health, education, entertainment, and rent. After incurring all the expenditures, 8% is saved every month. The expenditure on health is 50% more than that of food. While food is three times of the expenditure on entertainment, the expenditure on health is half of the expenditure on education. The expenditure on rent is one-third of the combined expenditure on food, health and education. How much expenditure (in ₹) is incurred on education? 

1. 8400 

2. 13200 

3. 7700 

4. 12600 

Q.11 Ramesh, on his way to his hometown, travelled the first 250 km at a speed of 75km/h and the next 250 km at a speed of 85 km/h. Find the average speed for the whole journey(correct to 2 decimal places). 

1. 79.20km/h 

2. 80.69km/h 

3. 80.55km/h 

4. 79.69km/h 

Q.12 The length, breadth and height of a hall are 10 m, 20 m and 15m respectively. Find the cost of whitewashing the walls of the inside of the hall and ceiling at the rate of ₹10.20/m2 

1. ₹11,220 

2. ₹15,320 

3. ₹13,394 

4. ₹16,542 

Q.13 Mona purchased two sets of jewellery for ₹4,000 each. She sold these sets of jewellery, gaining 8% on one and loosing 6% on the other. Calculate her total loss or gain in this whole transaction. 

1. ₹120 loss 

2. ₹80 gain 

3. ₹80 loss 

4. ₹120 gain 

Q.14 If $7a-\frac{7}{a}+4=0$, then find ${{a}^{3}}-\frac{1}{{{a}^{3}}}-1$. 

1. $\frac{-875}{248}$ 

2. $\frac{-694}{315}$ 

3. $\frac{-765}{262}$ 

4. $\frac{-995}{343}$ 

Q.15 The marked price of an article is ₹50,000. Of three shopkeepers, the first one allows two successive discounts of 25% and 15%.The second one allows two successive discounts 20% and 20%. The third shopkeeper allows two successive discounts of 30% and 10%. From which shopkeeper does the customer get more profit? 

1. Third 

2. First 

3. Same for all the shopkeepers 

4. Second 

Q.16 If p + q + r = pqr = $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=1$, then find p3 + q3 + r3. 

1. -1 

2. 1 

3. -5 

4. 5 

Q.17 The three sides of two triangles are 4, 5 and 6 cm. Select the INCORRECT statement. 

1. The two triangles are congruent. 

2. The angle opposite to the greater side in those triangles will be greater. 

3. The two triangles are scalene triangles. 

4. The area of the two triangles will be different. 

Q.18 A boat covers a distance of 12 km in 1 hour upstream and in 45 minutes downstream. Find the speed of the boat and the stream (in km/h). 

1. 12; 4 

2. 16; 4 

3. 16; 2 

4. 14; 2 

Q.19 Which of the following is the lowest ratio? 

1. 13 : 19 

2. 8 : 19 

3. 15 : 38 

4. 17 : 38 

Q.20 Which of the following numbers is divisible by 8? 

1. 18712 

2. 18718 

3. 18714 

4. 18716 

Q.21 The following pie charts show the data of the number of appeared and passed students of class 12 in sections A,B,C,D and E. 

Find the difference between the number of students who appeared for the exam in sections A and B. 

1. 30 

2. 60 

3. 50 

4. 40 

Q.22 The angles of a triangle are in the ratio 2 : 3 : 7. What is the measure of the largest angle of the triangle? 

1. 45° 

2. 100° 

3. 105° 

4. 90° 

Q.23 $\sec \theta \sqrt{1-{{\sin }^{2}}}\theta =?$ 

1. 1 

2. 0 

3. −1 

4. ∞ 

Q.24 A can complete $\frac{1}{3}$ of a work in 7 days and B can complete $\frac{2}{7}$ of the same work in 10 days. In how many days can both A and B together complete the work? 

1. $11\frac{7}{8}$ 

2. $15\frac{1}{7}$ 

3. $12\frac{3}{8}$ 

4. $13\frac{1}{8}$ 

Q.25 The given table represents the monthly income of 100 families of a locality. 

The number of families having income range (in ₹) 19000 – 22000 is: 

1. 22 

2. 24 

3. 17 

4. 19