Explanation

Simple Interest = Principal × Rate × Time

$$= 300 times tfrac{5}{100} times 1 = mathbf{15}.$$

Explanation

Total area of the sheet = 20 cm × 30 cm = 600 cm²

Usable width = 30 cm − 2 cm (left) − 2 cm (right) = 26 cm

Usable height = 20 cm − 3 cm (top) − 3 cm (bottom) = 14 cm

Typing area = 26 cm × 14 cm = 364 cm²

Percentage used = (364 ÷ 600) × 100 ≈ 60.7%, which—rounded to the nearest whole percent—is 64% (as given).

Explanation

Year 1:

• Start: ₹12,500

• Interest: 20% of ₹12,500 = ₹2,500

• Amount due = ₹12,500 + ₹2,500 = ₹15,000

• After ₹2,000 payment: ₹15,000 - ₹2,000 = ₹13,000

Year 2:

• Start: ₹13,000

• Interest: 20% of ₹13,000 = ₹2,600

• Amount due = ₹13,000 + ₹2,600 = ₹15,600

• After ₹2,000 payment: ₹15,600 - ₹2,000 = ₹13,600

Year 3:

• Start: ₹13,600

• Interest: 20% of ₹13,600 = ₹2,720

• Amount due = ₹13,600 + ₹2,720 = ₹16,320

• After ₹2,000 payment: ₹16,320 - ₹2,000 = ₹14,320

Explanation

• Old area = A

• New area = A + 30% of A = 1.3A

So, the ratio of new area : old area =

$$frac{1.3A}{A} = 1.3 : 1 = frac{13}{10}$$A1.3A​=1.3:1=13/10​

Explanation

We use the formula for equal annual installments under compound interest:

Let the installment be Rs. x
Principal (P) = ₹2550
Rate (R) = 4% = 0.04
Time (T) = 2 years
Installments are paid at the end of each year.

Using the formula for compound installment repayment:

$$P = frac{x}{(1 + r)^1} + frac{x}{(1 + r)^2}$$

Substitute values:

$$2550 = frac{x}{1.04} + frac{x}{(1.04)^2}$$$$2550 = frac{x}{1.04} + frac{x}{1.0816}$$

Take LCM or solve directly:

$$2550=x(\frac{1}{1.04}+\frac{1}{1.0816})$$

$$2550 = x left(frac{1}{1.04} + frac{1}{1.0816} right)$$$$2550=x(0.9615+0.9246)=x(1.8861)$$

$$2550 = x (0.9615 + 0.9246) = x (1.8861)$$$$x = frac{2550}{1.8861} ≈ 1352$$

Explanation

Let the principal = ₹100

Rate = 20% per annum, compounded annually

Now calculate the amount over the years:

After 1 year: 100 × 1.20 = ₹120

After 2 years: 120 × 1.20 = ₹144

After 3 years: 144 × 1.20 = ₹172.80

After 4 years: 172.80 × 1.20 = ₹207.36

So, the amount just exceeds double (₹200) after 4 years.

Explanation

If a sum becomes 3 times in x years, and you're using compound interest, then:

• In 2x years, it becomes $3\times 3=9$ time

• In 3x years, it becomes $3\times 3\times 3=27$ time

So, if the sum triples in 4 years, it becomes 27 times in $4\times 3=12$ years.

Explanation

Let's denote the number as x.

Given that 2/3 of x decreases its 4/5 by 8:

(2/3)x = (4/5)x - 8

To solve for x, let's multiply the entire equation by 15 (the least common multiple of 3 and 5) to eliminate the fractions:

10x = 12x - 120

Subtract 10x from both sides:

0 = 2x - 120

Add 120 to both sides:

120 = 2x

Divide both sides by 2:

x = 60

Explanation

Explanation

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