Numerical Ability Test - 6

Given:

Principal(P) = Rs. 8000

Rate of interest = 15%

Time = 1 months = 1/12 years 

Formula used:

Simple interest(SI) = \(\dfrac{P × R × T}{100}\)

Calculation:

SI = \(\dfrac{8000 \times 15 \times 1}{12 \times100}\)

⇒ SI = 100

∴ Simple interest = Rs. 100.

Given:

Principal is Rs. 12000 

Rate of interest, r = 20%

Numbers of years, n = 1.5 years

Concept:

If interest is compounded half yearly then the rate of interest (R) = R/2, and time (t years) = 2t 

Calculation:

Amount compounded half-yearly,

⇒ Rate = 20/2 = 10%

⇒ Time = 1.5 × 2 = 3

\(⇒ 12000 × {\left( {1 + 10/100} \right)^{2 × 1.5}}\)

⇒ 12000 × (1.1)³

⇒ 12000 × 1.331

⇒ 15972

Therefore the correct answer is 15972.

Given:

The difference between Simple Interest and Compound Interest = Rs.100

Rate = 6.25%

Time = 2 years

Difference = Principal × (R/100)²

⇒ 100 = Principal × (6.25/100)²

Principal = Rs.25600

Calculation:

Let the sum be Rs. P

We know that, C. I. \(= P\left[ {{{\left( {1 + \frac{r}{{100}}} \right)}^t} - 1} \right]\)

And SI = (P × r × t)/100

Where, P = principal, r = % rate of interest, t = time in years, SI = Simple interest, CI = Compound interest

\({\rm{C}}.{\rm{I\;}} = P\left[ {{{\left( {1 + \frac{6.25}{{100}}} \right)}^2} - 1} \right]\)

= 33P/256

S.I = P × 2 × 6.25/100 = P/8

According to question,

C.I – S.I = Rs. 100

\(\begin{array}{l} ⇒ \frac{{33P}}{{256}} - \frac{{P}}{{8}} = 100\\ ⇒ \frac{{33P - 32P}}{{256}} = 100 \end{array}\)

⇒P/256 = 100

Given:

A certain sum(principal) becomes Rs. 1400 in 7 years and Rs. 1610 in 10 years at simple interest(SI)

Formula used:

P = A - SI

P = Principal

A = Amount

Calculation:

According to the question:

Difference between the interest for 3 years = 1610 - 1400 = 210

Hence, SI for 1 year = 210/3 = 70

⇒ SI for 7 years = 70 × 7 = 490

P = 1400 - 490 = 910

∴ Sum = Rs. 910

Given:

The sum = 1200

The amount = 1560 

The time 3 years

Concept:

The simple interest = (Principle × Time × Rate)/100

Calculation:

Let be assume the rate of interest is R

⇒ 1560 - 1200 = (1200 × 3 × R)/100

⇒ 360 = 3600R/100

⇒ R = 10

⇒ In second condition let be assume time is T

⇒ 1120 - 800 = (800 × 10 × T)/100

⇒ 320 = 8000T/100

⇒ T = 4

∴ The required result will be 4.

Given:

The rate of interest = 4%

Formula used:

I = (P × R × T)/100    (Where, I = Simple interest, P = The principle, R = The rate, and T = The time)

Calculation:

Let be assume the principle is P and time is T

⇒ The simple interest = 3P/5

⇒ 3P/5 = (P × 4 × T)/100

⇒ 3P = 20PT/100

⇒ 3 = T/5

⇒ T = 15 years

Given 

A certain amount of money yields Rs.1250 interest under simple interest

Time = 2 years 

Formula Used 

Simple Interest = Principal × Rate × time/100

Calculation 

Let the certain principal amount be x

1250 = (x × 5 × 2 × 1)/100 

⇒ x = Rs 12500

∴ The certain principal amount is Rs 12500

Given:

Principal = Rs. 5000

Rate = 10%

Interest = Rs. 1500

Formula used:

SI = (P × R × T)/100

where, p is principal

R is rate

T is time 

Calculation:

SI = (P × R × T)/100

⇒ 1500 = (5000 × 10 × T)/100

⇒ 1500 = 500T

⇒ T = 3 years

∴ Required time is 3

Given:

Amount = 7 × sum

Number of years = 18 years

Formula used:

SI = (P × R × T)/100

SI → Simple interest, P → Principal, R → Rate, T → Time

Calculations:

Let the sum be 'x'

Amount = 7x

Simple interest = 7x - x = 6x

Hence, 6x = (x × 18 × R)/100

⇒ (6 × 100)/18 = R

⇒ R =  (100/3)% = 33.33%

∴ The rate of interest per annum is 33.33%

Given:

The ratio of Principal and Amount = 18 ∶ 25

Formula used:

Simple interest = (Principal × Rate × Time)/100

Calculation:

Let the Principal is Rs. 18x and Amount is Rs. 31x

So, Simple interest = Amount – Principal

⇒ 25x – 18x

⇒ 7x

⇒ 7x = (18x × Rate × 3.5)/100

⇒ 700 = 63 × Rate

⇒ 9 × Rate = 100

⇒ Rate = (100/9)%

⇒ Rate = 11.11%

∴ The rate of interest is 11.11%.