Numerical Ability Test

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Numerical Ability Test - 23

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Weekly Quiz Competition

Question 1
5 / -1

A sum becomes Rs. 34400 in 6 years on simple interest at the rate of 12 percent per annum. What is the total interest for the 6 years?

A
Rs. 16800

B
Rs. 17200

C
Rs. 14400

D
Rs. 15400

Solution

Given:

Total Amount = Rs 34400

Time = 6 years

R = 12%

Formula Used:

1. SI = PRT/100

2. SI = Total Amount - P

Where, P = Principal, R = Rate, T = Time(in years)

Calculation:

According to the question,

⇒ P = (34400 × 100)/172

⇒ P = Rs 20000

SI = 34400 - 20000 = Rs 14400

∴ The total interest for the 6 years is Rs 14400.
Question 2
5 / -1

In a store, Arun has two options to buy a mobile phone, either he can pay the full amount of Rs. 2,500 or he may buy at an instalment scheme, i.e. Rs. 520 in down payment and four equal instalments, rate of interest being charged at 25% p.a. simple interest. Arun buys a mobile phone on the instalment scheme. What is the monthly instalment for Arun?

A
Rs. 510

B
Rs. 530

C
Rs. 550

D
Rs. 520

Solution

Given:

After the down payment 2500 – 520= 1980

Rate % = 25 %

Total instalment = 4

Formula used:

calculation:

∴ Option 4 is the correct answer.
Question 3
5 / -1

What will be the amount due on ₹24,000 in 2 years when the rate of simple interest on successive years is 4% per annum and 5% per annum, respectively?

A
₹24,960

B
₹25,200

C
₹26,208

D
₹26,160

Solution

Given:

Principal amount (P) = ₹24,000

Rate of interest for first year = 4% per annum

Rate of interest for second year = 5% per annum

Formula Used:

Simple Interest (SI) = (P × R × T) / 100,

Where, P = Principle, R = rate, T = time

Calculation:

Rate for 1st year = 4%

Rate for 2nd year = 5%

So,in 2 year, effective rate of interest = 4% + 5% = 9%

Now,

Interest in 2 years

⇒ 24000 * 9%

⇒ 24000 * 9/100

⇒ 2160 Rs.

Thus, Amount after 2 years = 24000 + 2160 = 26160 rs.

The amount due on ₹24,000 in 2 years will be ₹26,160.
Question 4
5 / -1

What sum lent at 10% per annum simple interest would produce Rs. 200 as interest in 8 years?

A
Rs. 700

B
Rs. 500

C
Rs. 600

D
Rs. 250

Solution

Given:

Simple Interest = Rs. 200

Rate of interest = 10% p.a.

Time = 8 years

Formula used:

Where, P = Principal; R = Rate of interest; T = Time period

Calculation:

According to the question,

⇒ P = Rs. 250

The amount invested = Rs. 250

∴ Rs. 250 is the required answer.
Question 5
5 / -1

In 't' years, the simple interest earned on a certain amount at the rate of 10% per annum is 5/8^th of the principal amount. If the rate of interest is made three-fourth of 10% and the simple interest remains the same, which of the following statements is true about the changed value of time?

A
It remains the same as 't'.

B
It becomes three-fourth of the time 't'.

C

D

Solution

Given:

The rate of Interest is 10% and in 't' years received interest is 5/8^th of the principal amount

Concept Used:

Simple Interest (SI) = (P × R × t) / 100

Where, P = Principal, R = rate of interest and, t = time

Calculation:

Let, the principal = 8a and the interest received = 5a

Now, if the rate of interest is 3/4^th of 10% then R = 10% × 3/4 = 7.5%

According to the formula,

Required time (t) = (5a × 100) / (8a × 7.5) = 25/3 = years

∴ The correct answer is option 3
Question 6
5 / -1

What is the compound interest (in Rs.) on Rs. 4000 at 10% per annum for years, when interest is compounded annually ?

A
1050

B
1082

C
1260

D
1340

Solution

Concept use:

Amount = P(1 + r/n)^nt

SI = P × R × T/100

Compound interest = Final Amount - Principle

Calculation:

For the first 2 years, using compound interest formula:

A₁ = P(1 + r/n)^(nt)

= 4000(1 + 0.10/1)^{(1× 2)}= 4000(1.10)²

= 4000 × 1.21 = 4840 Rs.

Here, A₁ is the amount after 2 years.

For the next 0.5 years, we need to calculate simple interest on the amount A₁ = 4840 Rs:

I = P × R × T/100

= 4840 × 10 × 0.5 / 100 = 242 Rs.

Here, I is the interest for the remaining 0.5 years.

The total amount after 2.5 years, A2, is the sum of the amount after 2 years and the interest for the next 0.5 years:

A₂ = A₁ + I

= 4840 + 242 = 5082 Rs.

Finally, the compound interest is the difference between the total amount after 2.5 years and the original principal:

CI = A₂ - P = 5082 - 4000 = 1082 Rs.

So, the compound interest on Rs. 4000 at 10% per annum for 2.5 years, when interest is compounded annually, is indeed Rs. 1082.
Question 7
5 / -1

A man invests Rs. 5000 in a bond which gives compound interest at 4% per annum during the first year, 5% per annum during the second year and 10% during the third year. How much amount the man will get at the end of third year.

A
Rs. 6500

B
Rs. 5500

C
Rs. 5999

D
Rs. 6006

Solution

Calculation:

For the first year:

Interest rate is 4%.

Interest = Principal × Rate = Rs. 5000 × 4/100 = Rs. 200

So, the total amount at the end of the first year = Principal +

Interest = Rs. 5000 + Rs. 200 = Rs. 5200

For the second year: Interest rate is 5% and it's applied to the

total amount of Rs. 5200 accumulated at the end of first year.

Interest = Principal × Rate = Rs. 5200 × 5/100 = Rs. 260

So, the total amount at the end of the second year

= Principal + Interest = Rs. 5200 + Rs. 260 = Rs. 5460

For the third year: Interest rate is 10% and it's applied to the total amount of Rs. 5460 accumulated at the end of second year.

Interest = Principal × Rate = Rs. 5460 * 10/100 = Rs. 546

So, the total amount at the end of the third year = Principal +

Interest = Rs. 5460 + Rs. 546 = Rs. 6006

Therefore, the man will get Rs. 6006 at the end of third year.
Question 8
5 / -1

At what rate of compound interest (Compounding annually) per annum will a sum of Rs. 1,000 become Rs. 1,060.90 in 2 years?

A
2% per annum

B
4% per annum

C
3% per annum

D
5% per annum

Solution

Given:

Principal = Rs. 1000

Amount after 2 years = Rs. 1060.90

Concept:

We'll use the formula for compound interest, A = P(1 + r/n)^(not), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

Solution:

Given that interest is compounded annually, n = 1.

So the equation becomes A = P(1 + r)^t

Rearranging for r, we get r = (A/P)^(1/t) - 1 = (1060.90/1000)^(1/2) - 1 = 0.03 or 3%.

Therefore, the rate of compound interest per annum is 3%.
Question 9
5 / -1

If the difference between the compound interest, compounding annually and the simple interest on a certain sum of money at 5% per annum for 3 years is Rs.183, then what is the sum of money invested?

A
Rs.20,000

B
Rs.28,000

C
Rs.24,000

D
Rs.16,000

Solution

Given

Interest rate (r) = 5%

Time (t) = 3 years

Difference between Compound Interest and Simple Interest = Rs. 183

Formula:

If the difference between Compound Interest and Simple Interest for 3 years is given,

D = P × (R/100)2 (R% + 3)

Solution:

⇒ 183 = P × (5/100)² (R% + 3)

⇒ P = 183/(0.05)² × (5% + 3)

⇒ P = Rs.24,000

∴ The sum of money invested is Rs.24,000.
Question 10
5 / -1

Shyam wants to deposit Rs. 5000 for three years. The compound interest rate received for these years will be 20%, 30% and 10% respectively, then find the amount he will get at the end.

A
Rs. 8480

B
Rs. 8280

C
Rs. 8580

D
Rs. 8800

Solution

Given:

Shyam wants to deposit Rs. 5000 for three years.

The compound interest rate received for these years will be 20%, 30%, and 10% respectively.

Concept:

For a principal amount, P compounded annually for 3 years at rates of r₁, r₂, and r₃