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The logic follows here is :-

Thus, the correct answer is '292'.

The logic followed in the given pair:

In each pair, the second image has one extra vertical line going perpendicular to the number of horizontal lines in the first image.

So,

Similarly,

Hence, the correct answer is Option 4.

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. Some lions are pencils → False (It is possible but not definite)

II. Some pens are lions → False (It is possible but not definite)

III. Some pencils are lions→ False (It is possible but not definite)

Thus, none follows.

The logic follows here is :-

Thus, the correct answer is '454'.

i) P is to West of Q.

ii) R is to the South of P.

iii) T is to the North of Q and S is to the East of T.

Drawing the Diagram as per the given information:

Thus we can see point R is in South-West with respect to S.

Hence, the correct answer is "South-West".

Shortcut Trick

Total Simple Interest = Amount − Principal = ₹11,928 − ₹8,400 = ₹3,528

Simple Interest for 1 year = 7% of 8,400 = ₹588

Time = Total Interest ÷ Interest per year = 3528 ÷ 588 = 6 years

∴ The correct answer is 6 years.

Alternate Method

Given:

Principal (P) = ₹8,400

Amount (A) = ₹11,928

Rate (R) = 7% per annum

Formula Used:

Simple Interest (SI) = Amount − Principal

SI = (P × R × T) ÷ 100

Principal ₹8,400

• SI at 7% p.a. T = ? years

Amount ₹11,928

SI = ₹11,928 − ₹8,400 = ₹3,528

Calculations:

⇒ SI = 11,928 − 8,400 = 3,528

⇒ 3,528 = (8,400 × 7 × T) ÷ 100

⇒ 3,528 = 84 × 7 × T

⇒ 3,528 = 588 × T

⇒ T = 3,528 ÷ 588

⇒ T = 6

∴ The correct answer is 6 years.

Additional Information

Compound Interest (CI) Formula

When interest is compounded annually, Amount = P × (1 + R/100)^T. The CI is the difference between the Amount and the Principal.

Difference Between SI and CI for 2 Years

For a given principal P and rate R, the difference between CI and SI over 2 years is calculated as: D = P × (R/100)².

Rule of 72

A quick rule of thumb used to estimate the number of years required to double the invested money at a given annual fixed interest rate. Time ≈ 72 ÷ R.

Given

Pipe A can fill a tank in 80 min

Pipe B can fill a tank in 40 min

Concept

First find the tank filled by pipe A and B together in one minute. and then, reciprocate the answer to find the time taken  by both the pipes to filled the tank

Calculation

Tank filled by pipe A in 1 minute = 1/80

Tank filled by pipe B in 1 minute = 1/40

Tank filled  by pipe A and B in 1 minute together = (1/80) + (1/40)

⇒ (1 + 2)/80

⇒ 3/80

∴ Tank will be filled by A and B together in 80/3 minutes. i.e. $26{2\over3}$

Shortcut Trick

Profit of 60% implies Selling Price (SP) is 160% of Cost Price (CP).

Given SP = Rs 1180 → 160% = 1180

CP = 100% = (1180 ÷ 160) × 100

CP = 7.375 × 100 = Rs 737.5

∴ The correct option is A.

Alternate Method

Given:

Selling Price (SP₂) = Rs 1180

Profit % = 60%

Formula Used:

Cost Price (CP) = [SP ÷ (100 + Profit %)] × 100

CP (100%)

SP = 1180 +60% Profit Total SP = 160% of CP

⇒ Cost Price (CP) × (160 / 100) = 1180

⇒ CP × 1.6 = 1180

⇒ CP = 1180 ÷ 1.6

⇒ CP = 11800 ÷ 16

⇒ CP = 737.5

∴ The correct option is A.

Additional Information

Profit and Loss Percentage

Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Both are always calculated on the Cost Price unless stated otherwise.

Selling Price for Loss

When an item is sold at a loss of L%, the Selling Price = CP × (100 − L) ÷ 100.

Marked Price and Discount

Selling Price = Marked Price − Discount. Discount % is always calculated on the Marked Price (MP).

Given

Compound interest for 3 years = Rs. 4900

Compound interest for 5 years = Rs. 6400

Concept:

The formula for compound interest A = P(1 + r/n)^(nt), and that the difference in compound interest for two periods is the compound interest for the period in between.

Solution:

⇒ Compound interest for the period from the 3^rd year to the 5^th year = Rs. 6400 - Rs. 4900 = Rs. 1500

⇒ This amount is the interest for 2 years on the amount of Rs. 4900.

⇒ Using the compound interest formula, we have 4900(1 + r/100)² = 6400.

⇒ Solve for r to get r = 14$\frac{2}{7}$% per annum.

Therefore, the rate of interest per annum is 14$\frac{2}{7}$%.

Given:

$(\sqrt{162}\div \sqrt{147})\times(\sqrt{588}\div \sqrt{18})=?$

Calculation:

$(\sqrt{162}\div \sqrt{147})\times(\sqrt{588}\div \sqrt{18})$ =  x 

⇒ $(\dfrac{ \sqrt{162} }{ \sqrt{147}}) \times (\dfrac{ \sqrt{588} }{ \sqrt{18}})$ = x

⇒ $\sqrt{ \dfrac{162}{147} \times \dfrac{588}{18} }$ = x

⇒ x = $\sqrt{ 9 \times 4}$   = $\sqrt{ 36}$ = 6

∴ $(\sqrt{162}\div \sqrt{147})\times(\sqrt{588}\div \sqrt{18})$ = 6.