Numerical Ability Test - 17

Given:

Side of the larger cube = 5 cm

Side of each smaller cube = 1 cm

Formula Used:

Surface Area of a Cube = 6 × (side)²

Ratio = Surface Area of Larger Cube / Sum of Surface Areas of Smaller Cubes

Calculation:

Surface area of the larger cube:

Surface Area = 6 × 5²

⇒ 6 × 25 = 150 cm²

Number of smaller cubes = (5/1)³ = 125 cubes

Surface area of one smaller cube = 6 × 1² = 6 cm²

Total surface area of all smaller cubes = 6 × 125 = 750 cm²

Ratio = 150 : 750

⇒ 1 : 5

The ratio of the total surface area of the larger cube to the sum of the total surfaces of all the smaller cubes is 1:5.

Given:

Average earning for first 3 months = ₹24,328

April's earning = 50% more than ₹24,328

Average earning for the whole year = ₹76,867

Calculations:

April's earning = ₹24,328 + (50% of ₹24,328)

⇒ ₹24,328 + ₹12,164 = ₹36,492

Total earning for the first 4 months = (₹24,328 × 3) + ₹36,492

⇒ ₹72,984 + ₹36,492 = ₹1,09,476

Total earning for the whole year = ₹76,867 × 12 = ₹9,22,404

Earning from May to December = ₹9,22,404 - ₹1,09,476 = ₹8,12,928

Average earning per month from May to December = ₹8,12,928 / 8

⇒ ₹1,01,616

∴ Manav's average earning per month from May to December is ₹1,01,616.

Given:

Total voters = X

Votes cast = 80% of X = 0.8X

Invalid votes = 53

Winner's votes = 48% of X = 0.48X

Winner won by 1013 votes

Formula used:

Valid votes = Votes cast - Invalid votes

Winner's votes - Runner-up's votes = 1013

Calculations:

Valid votes = 0.8X - 53

Runner-up's votes = 0.48X - 1013

⇒ 0.48X + (0.48X - 1013) = 0.8X - 53

⇒ 0.96X - 1013 = 0.8X - 53

⇒ 0.96X - 0.8X = 1013 - 53

⇒ 0.16X = 960

⇒ X = 960 ÷ 0.16

⇒ X = 6000

∴ Total number of voters = 6000

Given:

A shopkeeper sells an item for ₹855.4 after giving two successive discounts of 90% and 75% on its marked price.

Formula used:

Let the marked price (MP) be x.

Selling price after discounts = MP × (1 - Discount1) × (1 - Discount2)

Cost Price (CP) = Selling Price / (1 + Profit%)

Calculation:

855.4 = x × (1 - 0.90) × (1 - 0.75)

⇒ 855.4 = x × 0.10 × 0.25

⇒ x = 855.4 / 0.025

⇒ x = 34216

Cost Price (CP) = Marked Price / (1 + Profit%)

⇒ CP = 34216 / 1.40

⇒ CP = 24440

∴ The correct answer is option 1.

Given:

Principal (P) = ₹8000

Rate (R) = 5% per annum

Amount (A) = ₹9261

Formula Used:

Compound Interest formula:

Calculation:

1.157625 = (1.05)ⁿ

(1.05)³ = (1.05)n

n = 3

The value of n is 3.

Given:

A can is completely filled with milk.

6 litre of milk is taken out of the can and is filled with water. This operation is performed four more times.

Now, the ratio of milk and water in the can is 32:211.

Formula Used:

Final amount of milk = Initial amount of milk × 

Calculation:

Let the volume of the can be V litre.

Given:

Average weight of X, Y, Z = 50 kg

Average weight of X, Y = 44.5 kg

Average weight of Y, Z = 53.5 kg

Weights of X, Y, Z are represented by p, q, r respectively.

Concept used:

Concept Used: Weighted Averages.

Calculation:

According to the question,

The Average weight of X, Y, and Z = 50 kg

⇒ p + q + r = 50 × 3

⇒ p + q + r = 150 .....(1)

The average weight of X and Y = 44.5 kg

⇒ p + q = 44.5 × 2

⇒ p + q = 89 .....(2)

The average weight of Y and Z = 53.5 kg

⇒ q + r = 53.5 × 2

⇒ q + r = 107 .....(3)

Solving these equations,

Subtract equation 2 from equation 1,

⇒ r = (p + q + r ) - (p + q)

⇒ r = 150 - 89 = 61     .....(4)

Subtract equation 4 from equation 3,

⇒ (q + r) - (r)

⇒ q = 107 - 61 = 46 .....(5)

Substitute q's value in equation 2,

⇒ p + q = 89

⇒ p + 46 = 89

⇒ p = 89 - 46  = 43 .....(6)

Given:

Word: IMPORTANT

Formula used:

Total permutations of the word = n! / (n₁! n₂! ... n_k!)

Where, n = total number of letters, n₁, n₂, ..., n_k = frequency of each repeated letter

Permutations with both T's together = Treat 'TT' as a single letter and calculate permutations

Permutations where T's are not together = Total permutations - Permutations with both T's together

Calculation:

Total letters in IMPORTANT = 9 (I, M, P, O, R, T, A, N, T)

Total permutations = 9! / 2!

⇒ Total permutations = 9! / 2

⇒ Total permutations = 362880 / 2

⇒ Total permutations = 181440

Considering 'TT' as a single letter, we have 8 letters: I, M, P, O, R, A, N, (TT)

Permutations with 'TT' together = 8!

⇒ Permutations with 'TT' together = 40320

Permutations where T's are not together = Total permutations - Permutations with 'TT' together

⇒ Permutations where T's are not together = 181440 - 40320

⇒ Permutations where T's are not together = 141120

∴ The correct answer is option 1.

Given:

Amar, Akram, and Vaibhav together can complete the work in 20 days.

Let Vaibhav's work rate be V (work units per day).

Then Akram's work rate = 2V and Amar's work rate = 3 × 2V = 6V.

Calculations:

Combined work rate of Amar, Akram, and Vaibhav = V + 2V + 6V = 9V.

In 20 days, they complete 1 work unit:

⇒ 20 × 9V = 1.

So, 180V = 1 → V = 1/180 work units per day.

Vaibhav alone can complete the work in:

⇒ Time = 1 / V = 1 / (1/180) = 180 days.

∴ Vaibhav alone can complete the work in 180 days.

Given:

The annual production in the cement industry is subject to business cycles. The production increases for two consecutive years consistently by 18% and decreases by 12% in the third year. This cycle repeats. Taking 2008 as the base year, we need to find the approximate effect on cement production in 2012.

Formula used:

Production in Year n = Production in Year (n-1) × (1 + Rate of Increase/Decrease)

Calculation:

Let the production in 2008 be 100 units.

2009: 100 × 1.18 = 118

2010: 118 × 1.18 = 139.24

2011: 139.24 × 0.88 = 122.5312

2012: 122.5312 × 1.18 = 144.586816

⇒ The production in 2012 is approximately 144.59 units.

⇒ The approximate percentage increase from 2008 to 2012 is:

⇒ ((144.59 - 100) / 100) × 100 = 44.59%

∴ The correct answer is option 3 (45% increase).