SSC CGL Quant – Ratio, Proportion, Partnership, Averages & Ages – Level 2 · Exam Level · Tier I Sprint

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SSC CGL Quant – Ratio, Proportion, Partnership, Averages & Ages – Level 2 · Exam Level · Tier I Sprint – 15 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
Two numbers are in the ratio 4 : 7. If 6 is added to each, the ratio becomes 2 : 3. The smaller number is:

Correct Answer: A [12]

Explanation:

(4x + 6)/(7x + 6) = 2/3 → 12x + 18 = 14x + 12 → x = 3 → 12 and 21.

2.  
₹ 6,300 is divided among A, B and C so that A gets half of B's share and B gets one-third of C's share. C's share is:

Correct Answer: B [₹ 4,200]

Explanation:

A : B : C = 1 : 2 : 6 → one part = 700 → C = ₹ 4,200.

3.  
A starts a business with ₹ 24,000. After 3 months B joins with ₹ 36,000. Out of a year-end profit of ₹ 25,500, B's share is:

Correct Answer: C [₹ 13,500]

Explanation:

24 × 12 : 36 × 9 = 288 : 324 = 8 : 9 → B = 9/17 × 25,500 = ₹ 13,500.

4.  
The average age of 30 students is 14 years. When the teacher is included, the average becomes 15 years. The teacher's age is:

Correct Answer: D [45 years]

Explanation:

Newcomer: 14 + 31 × 1 = 45.

5.  
The average of 10 numbers falls by 3 when one number, 75, is replaced by a new number. The new number is:

Correct Answer: A [45]

Explanation:

Replacement: 75 + 10 × (−3) = 45.

6.  
The ratio of the present ages of two sisters is 4 : 5. Five years ago it was 3 : 4. The present age of the elder sister is:

Correct Answer: D [25 years]

Explanation:

Both ratios have gap 1 → 1 part = 5 years → 20 and 25.

7.  
Two-quantity comparison
Quantity I: the fourth proportional to 3, 5 and 12
Quantity II: the mean proportional between 16 and 25

Correct Answer: C [Quantity I = Quantity II]

Explanation:

QI = 5 × 12/3 = 20; QII = √400 = 20.

8.  
Match the following
P. duplicate ratio of 2 : 3 Q. sub-duplicate ratio of 49 : 64 R. triplicate ratio of 1 : 2
1. 7 : 8 2. 1 : 8 3. 4 : 9

Correct Answer: B [P-3, Q-1, R-2]

Explanation:

2² : 3² = 4 : 9; √49 : √64 = 7 : 8; 1³ : 2³ = 1 : 8.

9.  
Trick Spotterthe fastest way to find the average of 47, 53, 49, 55 and 56 is:

Correct Answer: C [assume 50; deviations add to +10, so 50 + 2 = 52]

Explanation:

Deviation Balance: −3 + 3 − 1 + 5 + 6 = +10, so 50 + 10/5 = 52.

10.  
Spot My Mistake“20 students average 50 marks and 30 students average 60 marks, so all 50 students average (50 + 60)/2 = 55.” The correct average is:

Correct Answer: D [56]

Explanation:

Weighted: (1,000 + 1,800)/50 = 56.

11.  
A purse has ₹ 1, 50-paise and 25-paise coins in the ratio 1 : 2 : 3 by number, worth ₹ 110 in all. How many 50-paise coins are there?

Correct Answer: C [80]

Explanation:

One set (1 + 2 + 3 coins) = ₹ 1 + ₹ 1 + ₹ 0.75 = ₹ 2.75 → 40 sets → 80 coins of 50 paise.

12.  
The average of 7 consecutive odd numbers is 31. The largest of them is:

Correct Answer: B [37]

Explanation:

The middle (4th) number is 31; the largest is 31 + 3 × 2 = 37.

13.  
Diagram-basedThe bar chart shows the marks of five students. What is their average?

Correct Answer: A [68]

Explanation:

Assume 70: deviations −6, +2, −12, +10, −4 → −10 → 70 − 2 = 68.

14.  
Assertion–Reason
A: If every value in a list is increased by 5, the average increases by 5.
R: The average is the sum divided by the number of values, and the sum increases by 5n.

Correct Answer: B [Both A and R are true and R explains A]

Explanation:

(S + 5n)/n = S/n + 5 – exactly what R says.

15.  
Odd one out2 : 3, 4 : 6, 10 : 15, 6 : 8

Correct Answer: A [6 : 8]

Explanation:

6 : 8 = 3 : 4; all the others equal 2 : 3.

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