Chapter 7: Comparing Quantities

Solution:-

If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then 60 % of A is equal to C.

From the question it is given that, A is increased by 20%, it equals B = A + (20/100) × A

B is decreased by 50%, it equals C = B – (50/100) × B

Then,

A (1 + (1/5)) = B

(6/5) A = B … [equation i]

Now,

B (1 – (1/2)) = C

½B = C

B = 2C … [equation ii]

Substitute equation (ii) in equation (i)

(6/5)A = 2C

C = (6/10) A

C = ((6 × 10)/(10 × 10))A

C = (60/100) × A

C = 60% of A

Solution:-

Interest = (P × R × T)/100, where

T is Time period

R % is Rate of Interest and

P is Principal.

Solution:-

The difference of interest for 2 years and 3 years on a sum of ₹ 2100 at 8% per annum is ₹ 168.

From the question it is given that,

P = ₹ 2100

Time = 2 years

Rate = 8%

Then, we know the formula of Simple interest I = (P × R × T)/100

I = (2100 × 2 × 8)/100

I = 33600/100

I = ₹ 336

Then,

Time = 3 years

I = (P × R × T)/100

I = (2100 × 3× 8)/100

I = 50400/100

I = ₹ 504

The difference of interest for 2 years and 3 years = 3 years – 2 years

= ₹ 504 – ₹ 336

= ₹ 168

Solution:-

To convert a fraction into a per cent, we multiply it by 100.

Solution:-

To convert a decimal into a per cent, we shift the decimal point two places to the right.

Solution:-

The sum of interest on a sum of ₹ 2000 at the rate of 6% per annum for 1½ years and 2 years is ₹ 420.

From the question it is given that, P = 2000, R = 6% and T = 1½ years

As we know that,

I = (P × R × T)/100

I = (2000 × 6 × 3)/ (100 × 2)

I = ₹ 180

For 2 years,

I = (P × R × T)/100

I = (2000 × 6 × 2)/ (100)

I = ₹ 240

Then, sum = 180 + 240 = ₹ 420

Solution:-

When converted into percentage, the value of 6.5 is more than 100%.

Given, 6.5

= 6.5 × 100

= 650%

In questions 58 and 59, copy each number line. Fill in the blanks so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.

58.

Solution:-

We know that, Percentage = Fraction × 100

Then, Fraction = Percentage /100

Decimal = Percentage/ 100

59.

Solution:-

We know that, Percentage = Fraction × 100

Then, Fraction = Percentage /100

Decimal = Percentage/ 100

In questions 60 to 79, state whether the statements are True or False.

Ans:

For fraction $\dfrac{1}{10}$ and decimal $0.1$, the percent is $10\%$.

For percent $20\%$ and decimal $0.2$, the fraction is $\dfrac{2}{10}$.

For $30\%$ and $\dfrac{3}{10}$ fraction, the decimal is $0.3$.

For \[0.4\] decimal, the fraction is $\dfrac{4}{10}$ and percent is \[40\%\]

For \[50\%\], the fraction is \[\dfrac{1}{2}\] and the decimal is \[0.5\].

For \[\dfrac{3}{5}\] fraction, the percent is \[60\%\] and decimal is \[0.6\].

For \[0.7\] decimal, the percent is \[70\%\] and fraction \[\dfrac{7}{10}\]

For \[80\%\] the fraction is \[4/5\] and decimal is \[0.8\]

For \[\dfrac{9}{10}\] fraction, the percent is \[90\%\] and decimal is \[0.9\]

Ans:

To find out:

The percent, fraction and decimal on the number line:

For $\dfrac{1}{8}$ fraction, the percent is $12.5\%$ and decimal is $0.125$

For $25\%$ the fraction is $\dfrac{1}{4}$ and decimal is $0.25$

For $37.5\%$ the fraction is $\dfrac{3}{8}$ and decimal is $0.375$

For $50\%$ the fraction is $\dfrac{1}{2}$ and decimal is $0.5$

For the fraction $\dfrac{5}{8}$, the percent is $62.5\%$ and decimal is $0.625$

For the decimal $0.75$, the percent is $75\%$ and fraction is $\dfrac{3}{4}$

For $87.5\%$, the fraction is $\dfrac{7}{8}$ and decimal is $0.875$

For $1$, the percent is $100\%$ 

In questions 60 to 79, state whether the statements are True or False.

Solution:-

True

= (2/3) × 100%

= 200/3

=