CSIR ASO/SO (Numerical Ability): Memory Based Test: (Held on: 6th Feb 2024) (Previous Year Paper)

GIVEN:

Diameter of the conical cap = 32 cm

Height = 12 cm

Cost of painting is 77 paise per cm²

CONCEPT:

Slant height to be found for CSA

FORMULA USED:

l² = r² + h²

Curved surface area = πrl

CALCULATION:

Given the diameter of the conical cap = 32 cm

⇒ radius r = 16 cm.

Slant height l can be found as

⇒ l² = 16² + 12²

⇒ l² = 256 + 144

⇒ l² = 400

⇒ l = 20

⇒ Curved surface area that need to be painted = πrl = π × (16) × (20) = 320 π

Cost of painting is 77 paise per cm²

Hence,

Cost for painting 320 π cm²

⇒ 77 × 320 π cm² paise

⇒ 77 × (320) × (22/7)

⇒ 77440 paise

⇒ 774.4 rupees

∴ Cost of the paiting the curved surface area of the cap os Rs. 774.4

Given:

Speed of River = 2 kmph

Distance upstream = 10 km

Speed of boat = 22 kmph

Formula Used:

Distance = T (x² – y²)/ 2x

Calculations:

Let the time taken be T hours.

Speed of stream (y) = 2 kmph

Upstream speed = 20 kmph

Downstream speed = 24 kmph

According to the formula,

Distance = T (x² – y²)/ 2x

⇒ 10 = T × (22² – 2²)/ 2 × 22

⇒ 440 = T(480)

⇒ T = 440/480 = 11/12 hour

⇒ 11/12 hour → 11/12 × 60 = 55 minutes.

∴ The answer is 55 minutes.

Calculation:

Statement 1:

Rice production by A in the year 2016 = 50 lakh tonnes

Rice production by C in the year 2020 = 45 lakh tonnes

Statement 1 is incorrect.

Statement 2:

Rice production by B in the year 2018 = 50 lakh tonnes

Rice production by A in the year 2018 = 55 lakh tonnes

Rice production by C in the year 2018 = 60 lakh tonnes

Statement 2 is incorrect.

Statement 3:

Rice production in the year 2017 = 40 + 60 + 50 = 150 lakh tonnes

Rice production in the year 2018 = 55 + 50 + 60 = 165 lakh tonnes

Statement 3 is incorrect.

Statement 4:

Rice production by B in the year 2017 = 60 lakh tonnes

Rice production by A in the year 2020 = 60 lakh tonnes

Statement 4 is correct.

∴ The correct option is 4.

Calculation

⇒ (37 × 3) + $\sqrt{1024}$ = ? - (17 × 4) + $\sqrt{729}$ - 66

⇒ 111 + 32 = ? - 68 + 27 - 66

⇒ 143 = ? - 68 + 27 - 66

⇒ ? = 143 + 134 - 27

⇒ ? = 277 - 27

⇒ ? = 250

The answer is 250.

Given:

Rate of interest = 32%

Time =  2 years

Compound interest = 6681.6

Formula used:

CI = P[1 + (R/100)]^T - P

Where, CI = Compound interest

R = Rate of interest

P = Principle and T = Time

Calculation:

⇒ 6681.6 = P[1 + (32/100)]² - P

⇒ 6681.6 = P × (132/100)² - P

⇒ 6681.6 = P × (1.32 × 1.32) - P

⇒ 6681.6 = 1.7424 × P - P

⇒ 6681.6 = 0.7424P

⇒ P = 6681.6/0.7424 = 9000

Hence, the value of the principle is Rs. 9000.

Given:

Cost price of article = a + 1000

Profit = Rs. 1000

Discount = 12.5%

Solution:

Marked price = 160%  of (a + 1000) = 8/5(a + 1000)

Selling price = 7/8 of (8/5(a + 1000) = 7/5 of (a + 1000)   (12.5% = 1/8)

Now,

Profit = SP - CP

1000 = 7/5of (a + 1000) - (a +1000)

1000 = (2a + 2000)/5

2a + 2000 = 5000

2a = 3000

a = 1500

Selling price of X = 7/5(a + 1000) = 3500

Now,

Cost price = a + 500 = 2000

Selling price of B is 14.28% less than selling price of article X

Selling price = 6/7 x 3500  (14.28% = 1/7)

= 3000

Profit% = (SP - CP)/CP x100 = (3000 - 2000)/2000 x 100 = 50%

Hence option (3) is correct.

Given:

The expression $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $\left(\frac{1}{9}+\frac{1}{8}\right)+\left(\frac{63}{56} \times \frac{48}{72}\right)$

Concept used:

⇒ BODMAS rule

Calculation:

⇒ $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $(\frac{8 + 9 }{72}) + (\frac{9}{8} \times \frac{2}{3})$

⇒ $\frac{1}{7} \times \frac{1}{8} \div \frac{72}{51}$ of $\frac{17 }{72} + \frac{3}{4}$

⇒ $\frac{1}{7} \times \frac{1}{8} \div( \frac{72}{51} \times \frac{17}{72})$ $+ \ \frac{3}{4}$

⇒ $\frac{1}{7} \times( \frac{1}{8} \div \frac{1}{3}) + \frac{3}{4}$

⇒ $\frac{1}{7} \times \frac{3}{8} + \frac{3}{4}$

⇒ $\frac{3}{56} + \frac{3}{4}$

⇒ $\frac{45}{56}$

Hence, the value of expression is 45/56.

Given:

Discount = 10%, 15% and 10%

SP = 2754

Formula used:

Profit = SP – CP

Discount% = Discount/MP × 100

Calculation:

Let the marked price be MP 

⇒ MP × (9/10)(17/20)(9/10) = 2754

⇒ MP × 1377/2000 = 2754

MP = 4000

The answer is 4000.

Given:

X can do a work = 270 days

Concept used:

Total Work = Efficiency × Time

Calculation:

According to the question,

⇒ X × 270 = X × 55 + Y × 215

⇒ X × (270 - 55) = Y × 215

⇒ X × 215 = Y × 215

⇒ $\dfrac{\text{X}}{\text{Y}}$ =$\dfrac{215 }{215}$= $\dfrac{1 }{1}$

∴ Efficiency of X: Efficiency of Y = 1: 1

Now, Total work = X × 270 = 1 × 270 = 270 unit

Time is taken by X and Y together = $\dfrac{270 }{1+1}$ = $\dfrac{270 }{2}$ = 135 days

∴ The time is taken by X and Y together is 135 days.

Given:

Height = 5 m

Cost of whitewashing 4 walls at Rs. 2.50 per sq m = Rs. 200

Cost of carpeting the floor = Rs. 5/m²

Calculation:

Let breadth be x meter

⇒ Length = 3x meter

Area of 2 walls along length side = 2 × height × length = 2 × 5 × 3x = 30x

Area of 2 walls along breadth side = 2 × height × breadth = 2 × 5 × x = 10x

Total area of 4 walls = 30x + 10x = 40x

Now, 40x × Rs. 2.5 = Rs. 200

⇒ 40x = 80

⇒ x = 2

Breadth = 2 meter

Length = 2 × 3 = 6 meter

Now, area of floor = length × breadth = (6 × 2) m² = 12 m²

Cost of carpeting the floor at Rs. 5/m² = 12 × 5 = Rs. 60

∴ Cost of carpeting the floor is Rs. 60

Given:

Hours worked per day in first week = 4

Hours worked per day in second week = 5

Hours worked per day in third and fourth week = 6

Rate = Rs. 100 for every 30 minutes 

Concept:

In these type of questions we calculate total hours worked and multiply them by the rate.

Formula:

Amount = Total hours × Price per hour

Calculations:

Hours worked in first week = 4 × 7

⇒ 28 hours 

Hours worked in second week = 5 × 7

⇒ 35 hours

Hours worked in third week = 6 × 7

⇒ 42 hours 

Hours worked in fourth week = 6 × 7

⇒ 42 hours 

∴ Total hours worked = 28 + 35 + 42 + 42

⇒ 147 hours

Rate = Rs. 100 for every 30 minutes

⇒ Rs. 100 × 2 for every hour

⇒ Rs. 200 per hour

∴ Amount that the worker will receive = 147 × 200

⇒ Rs. 29400

DIRECTIONS: What approximate value will come in place of the question mark (?) in the following question?

√5456 × √2120 ÷ √460 = ?

Calculation:

First, approximate the square roots of the given numbers:

√5456 ≈ 74 (since 74 × 74 = 5476, which is close to 5456)

√2120 ≈ 46 (since 46 × 46 = 2116, which is close to 2120)

√460 ≈ 21.5 (since 21.5 × 21.5 = 462.25, which is close to 460)

Now, substitute these approximations into the equation:

√5456 × √2120 ÷ √460 ≈ 74 × 46 ÷ 21.5

Calculate the numerator:

74 × 46 = 3404

Now, divide by the denominator:

3404 ÷ 21.5 ≈ 158.32 ≈ 159

Therefore, the approximate value that will come in place of the question mark is 159.

Calculation

⇒ 1100% of 44 + 115% of 240 = ? - 24

⇒ 484 + 23 × 12 = ? - 24

⇒ 484 + 276 + 24 = ?

⇒ 784 = ?

The answer is 784.

Given:

Total number of 'Vadas' was 12.

Calculation:

Let's assume that the consecutive 3-even numbers be 2x, (2x + 2), (2x + 4)

Now, according to the question

⇒ 2x +  (2x + 2) + (2x + 4) = 12

⇒ 6x + 6 = 12

⇒ x = 1

So, the numbers are 2, 4, 6

∴ The maximum number of Vadas kept in a plate is 6

Shortcut Trick

Profit share is directly proportional to Capital × Time.

Aman's 1 profit ratio part = 4000 × 12 = 48000.

Bunty's profit (3 parts) = 3 × 48000 = 144000 ⇒ Bunty's Capital = 144000 ÷ 5 = Rs. 28800.

Chaman's profit (7 parts) = 7 × 48000 = 336000 ⇒ Chaman's Capital = 336000 ÷ 8 = Rs. 42000.

Difference in their capitals = 42000 − 28800 = 13200.

∴ The correct answer is Rs. 13200.

Alternate Method

Given:

Aman's Capital (C_A) = Rs. 4000

Time of investment for Aman (T_A) = 12 months

Bunty joined after 7 months, so Time (T_B) = 12 − 7 = 5 months

Chaman joined after 4 months, so Time (T_C) = 12 − 4 = 8 months

Profit Ratio = 1 : 3 : 7

Formula Used:

Profit Ratio = (C_A × T_A) : (C_B × T_B) : (C_C × T_C)

Aman Cap: ₹4000 Time: 12 mo

Ratio: 1 = 48000 units

Bunty Cap: ? Time: 5 mo

Ratio: 3 = 144000 units

Chaman Cap: ? Time: 8 mo

Ratio: 7 = 336000 units

Calculations:

⇒ Aman's profit equivalent = 4000 × 12 = 48000

⇒ As per the ratio, 1 unit of profit is represented by 48000.

⇒ Bunty's profit equivalent = 3 units = 3 × 48000 = 144000

⇒ Bunty's Capital × 5 = 144000

⇒ Bunty's Capital = 144000 ÷ 5 = 28800

⇒ Chaman's profit equivalent = 7 units = 7 × 48000 = 336000

⇒ Chaman's Capital × 8 = 336000

⇒ Chaman's Capital = 336000 ÷ 8 = 42000

⇒ Difference = 42000 − 28800 = 13200

∴ The correct answer is Rs. 13200.

Additional Information

Basic Profit Division Rule

If partners invest different amounts for varying time periods, the total profit is distributed in the ratio of the product of their invested capital and the duration of investment: (C₁ × T₁ : C₂ × T₂ : C₃ × T₃).

Equivalent Capital

Equivalent capital represents the total amount that would need to be invested for a standard unit of time (like 1 month) to yield the exact same final profit share.

Working vs Sleeping Partners

A working partner actively manages the business and usually takes a fixed percentage of the profit or a fixed salary before the rest of the profit is divided among all partners based on their investments. A sleeping partner merely invests capital.

Let the two numbers be x and y.

Given,

xy = 2500

And x is four times y.

⇒ x = 4y      ----(1)

Putting the value of x in (1), we get

⇒ 4y² = 2500

⇒ y² = 625

⇒ y = 25

The numbers are x = 4 × y = 100 and y = 25

Sum of two numbers = 100 + 25 = 125

Shortcut Trick

Speed ratio P : Q is 11 : 16. Difference = 5 units = 25 km/h ⇒ 1 unit = 5 km/h.

Speed of P = 11 × 5 = 55 km/h; Speed of Q = 16 × 5 = 80 km/h.

Relative speed = 55 + 80 = 135 km/h. Meeting time = 1 hr 36 min = 8/5 hr.

Total Distance XY = 135 × (8/5) = 27 × 8 = 216 km.

Time for P = Distance ÷ Speed of P = 216 / 55 hr.

∴ The correct answer is 216/55 hr.

Alternate Method

Given: Speed ratio P:Q = 11:16, Speed difference = 25 km/h, Meeting time = 1 hr 36 min.

Formula Used: Speed = Distance ÷ Time; Relative Speed (Opposite) = S₁ + S₂.

⇒ Let speeds be 11k and 16k. Difference = 16k − 11k = 5k.

⇒ 5k = 25 ⇒ k = 5 km/h.

⇒ Speed of P = 55 km/h, Speed of Q = 80 km/h.

⇒ Meeting time = 1 + 36/60 = 1 + 3/5 = 8/5 hours.

⇒ Total Distance = Relative Speed × Meeting Time = (55 + 80) × (8/5) = 135 × (8/5) = 216 km.

⇒ Time taken by P = Total Distance ÷ Speed of P = 216 / 55 hr.

∴ The correct answer is 216/55 hr.

Additional Information

Relative Speed

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂).

Meeting Time Logic

Total Distance = Relative Speed × Time taken to meet, provided they start moving at the same time.

Time and Speed Relation

For a constant distance, the time taken is inversely proportional to the speed (T ∝ 1/S).

Given:

The perimeters of two squares plots are 52 cm and 20cm

Concept used:

The perimeter of square = 4 × side

The area of a square = (side)2

Calculation:

Side of the first square = 52 ÷ 4 = 13 cm and

Side of the second square = 20 ÷ 4 = 5 cm

Now, the difference in their areas = 13² – 5² = 144 cm²

Then, sides of the new square = √144 = 12 cm

Now, perimeter of new square = 4 × 12 = 48 cm

∴ The perimeter of the third square is 48 cm

Given:

The difference between simple interest and compound interest (compounding of interest is done annually) on a certain sum of money for 3 years at the rate of 20 percent per annum is Rs. 192. 

Formula used:

Difference between CI and SI in 3 yr = P( R /100)² {( R/100) + 3}

Calculation:

Let the principal is P

As per the question,

⇒ 192 = P( 20 /100)2 {( 20/100) + 3}

⇒ 192 = P( 1/5)2 {( 1/5 + 3}

⇒ P = 4800 / 3.2

⇒ P = Rs 1500

∴ The correct option is 3

Given:

Mansi and Taruna have money in the ratio 5: 7

Taruna and Renu have it in the ratio 8 : 11

Taruna has Rs. 2240

Calculation:

Mansi: Taruna = 5: 7 ....(× 8)

Taruna: Renu = 8: 11 ....(× 7)

Mansi: Taruna: Renu = 40: 56: 77

56 → 2240

1 → 2240/56 = 40

77 → 77 × 40 = 3080

The answer is 3080.

Given:

The average age of 4 members 5 years ago = 22 years

The average age of the family is the same as what it was 5 years ago after the baby is born.

Formula used:

The sum of ages = Average × Number of family members

Calculation:

Total age of 4 members of the family at present = 27 × 4 years

⇒ 108 years

The present age of 5 members would have been = 22 × 5 = 110

Age of baby = (110 - 108) years

⇒ 2 year

∴ The age of baby is 2 year

Given:

Rs. 3550 is divided into X, Y and Z

three times of X's share is equal to 5 times of Y's share and 7 times of Z's share.

Solution:

3X = 5Y

⇒ Y = $\dfrac{3X}{5}$

3X = 7Z

⇒ Z = $\dfrac{3X}{7}$

X + Y + Z = 3550

⇒ X + $\dfrac{3X}{5}$ + $\dfrac{3X}{7}$ = 3550

⇒ 35X + 21X + 15X = 124250

⇒ X = $\dfrac{124250}{71}$ = 1750

Share of X = Rs. 1750

GIVEN:

Sum of their monthly salary = Rs60000

A's expenditure = 80% of his salary 

B's expenditure = 90% of his salary

A's savings = B's savings

EXPLANATION:

Let A's salary be x

∴ B's salary = 60000 - x

A's savings = 20% of x = $\frac{x}{5}$

B's savings = 10% of (60000 - x) = $\frac{60000 - x}{10}$

$\therefore \frac{x}{5} = \frac{60000 - x}{10}$ ⇒ $x = 20000$

B's salary = $60000 - 20000 = 40000$

Alternate Method

$20\% \ of \ A = 10\% \ of \ B$

$\Rightarrow \frac{A}{B} = \frac{1}{2}$

$\Rightarrow A + B = 3 \space ratio$

$3\space ratio = 60000 \Rightarrow 1\space ratio = 20000$

$B's\space salary = 2\space ratio = 40000$

Given:

Ravi spends 70% of his income. His income increases by 25% and his expenditure also increases by 10%

Concept used:

Income - Expenses = Saving

Calculation:

Let the income be 100p

According to the question:

Ravi spends 70% of his income

Expenses = 70p

⇒ 100p - 70p = 30p

Savings = 30p

Income increases by 25% 

⇒ 100p + 25p = 125p

Expenditure increases by 10% 

⇒ 70p + 70p × 10/100 = 77p 

Savings = 125p - 77p = 48

Saving Increase% = (48 - 30)/30 × 100

= 60%

The answer is 60%

Calculation:

Total number of donuts sold by stores P and R together in October = 125 + 960

⇒ 1085

Total number of donuts sold by stores R and Q together in October = 905 + 960

⇒ 1865

Ratio = 1085 : 1865

⇒ 217 : 373

∴ The required answer is 217 : 373.