The approximate mass of the earth is $5.97 \times 10^{24}$ kg. How many times is the earth heavier than a sumo wrestler who weighs 125 kg? Give your answer in standard form correct to 3 significant figures. A mobile phone can be bought online at a price of US$350. The same type of mobile phone is sold in Singapore at S$600. A local shop owner decides to sell the same type of mobile phone at a discount such that its price is equivalent to what a buyer pays online. Given that US$1 = S$1.36, calculate the percentage of discount he has to offer. A train travels for 68 km at an average speed of 51 km/h. It then traveled for another 20 km at an average speed of 40 km/h before reaching its destination. Calculate the average speed for the whole journey. In the year 2020, there are 250 male employees and 300 female employees in an office. In the year 2019, the number of male employees was 130% of the current male employees. In the year 2019, the number of female employees was 65% of the current female employees. Find the difference in the number of male and female employees in the year 2019 as a percentage of the number of female employees in that year.

1. Form and calculate the ratio of the earth's mass to the sumo wrestler's mass.

$\frac{5.97 \times 10^{24}}{125}=4.776\times 10^{22}$

2. Round the answer to 3 significant figures and keep it in standard form.

$4.776\times 10^{22} \approx 4.78\times 10^{22} \quad \text{(3 s.f.)}$

1. Convert the online price to Singapore dollars.

Online price in Singapore dollars:
$350 \times 1.36 = 476$
So the equivalent online price is S$476.

2. Find the discount amount needed from the Singapore price.

Discount needed:
$600 - 476 = 124$
So the shop owner must reduce the price by S$124.

3. Express the discount as a percentage of the original Singapore price.

Percentage discount:
$\frac{124}{600} \times 100\% = 20.666\ldots\%$
$\approx 20.7\%$

1. Find the total distance travelled.

Total distance
$=68+20=88\text{ km}$

2. Find the total time taken for the two parts of the journey.

Using $\text{time}=\dfrac{\text{distance}}{\text{speed}}$,
$\text{Total time}=\frac{68}{51}+\frac{20}{40}$
$=\frac{4}{3}+\frac{1}{2}=\frac{11}{6}\text{ h}$

3. Calculate the average speed for the whole journey.

Average speed
$=\frac{\text{total distance}}{\text{total time}}$
$=\frac{88}{\frac{11}{6}}=88\times\frac{6}{11}=48\text{ km/h}$

1. Find the number of male employees in 2019.

Number of male employees in 2019
$=130\%\times 250=\frac{130}{100}\times 250=325$

2. Find the number of female employees in 2019.

Number of female employees in 2019
$=65\%\times 300=\frac{65}{100}\times 300=195$

3. Express the difference as a percentage of the number of female employees in 2019.

Difference
$=325-195=130$
Required percentage
$=\frac{130}{195}\times 100\%=66.666\ldots\%$
$\approx 66.7\%$