case /data -based (4 Marks)

Question 14 Marks

The Bureau of Indian Standards $(BIS),$ certiies the purity of gold jewellery using hallmark codes.
The $BIS$ hallmark codes for gold jewellery are given below.

Hallmark code	Purity of gold jewellery (Carats)
$22K916$	$22$
$18K750$	$18$
$14K585$	$14$

$1.$ Riya purchased a gold necklace weighing $20 g$ hallmarked $18K750.$ How many grams of pure gold are in the necklace$?$

Answer

$10. 15$ or $15 g$

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Question 24 Marks

Carat $(K)$ is a unit to measure the purity of gold. The higher the carat, the purer the gold. $24K$ gold is considered as the purest gold with no traces of any other metal in it.
$22K$ gold has $2$ parts other metals present in it.
$1.$ Puneet is a jeweller. He wants to make $18K$ gold jewellery from $22K$ gold.
What percent of other metals are to be added to the $22K$ gold$?$
$2.$ Countries have their own minimum acceptance standard for an item to be called a gold item.
The minimum accepted standard of gold is $10$ carat in the $US$ and $8$ carat in Denmark.
What is the difference in percentage of gold between the standards set by the two countries$?$
Round your answer to the nearest whole number.

Answer

$8. 16.66$ or $16.66 \%$
$17$ or $17 \%$
$9. 8$ or $8\%$

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Question 34 Marks

An online game has $50$ levels. A gamer is in the Gold team until he cross of the $\frac{3}{4}$ total levels. After that he is in the Platinum team.
This table shows the rewards unlocked after completing various levels.

Levels completed	Rewards
More than or equal to $\frac{4}{5}$ levels	Jeep
More than $\frac{3}{5}$ levels but less than $\frac{4}{5}$ levels	Dress
More than $\frac{2}{5}$ levels but less than $\frac{3}{5}$ levels	Face mask
More than $\frac{1}{5}$ levels but less than $\frac{2}{5}$ levels	Badge

$1.$ Mita completed $37$ levels.
Which reward would she get$?$ Justify your answer.
$2.$ Mayank is at level $15$ in the game. In which team, would he play$?$

Answer

$6.$ Mentions ‘Dress’ with valid justiication
● She will get a dress because she completed $37$ levels which is more than $\frac{3}{5}$ but less than $\frac{4}{5}$ of the game levels.
● She will get a dress as she completed more than $\frac{3}{5}$ but less than $\frac{4}{5}$ of the game levels.
● She will get a dress. $37$ out of $50$ is more than $30$ out of $50$ but less than $40$ out of $50.$
$7.$ Gold or Gold team

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Question 44 Marks

Insulin is a hormone made by the pancreas in the human body. It helps to regulate blood sugar level and absorbs glucose to get energy. The number of required units of insulin varies according to the individual.
In some cases, an individual body is not able to produce suficient amount of insulin. For those
individuals, supplementary units of insulin are injected into the body.
$1.$ A doctor uses this formula to calculate the daily insulin units required for Prakhar’s body.
Daily insulin requirement $($units$) = 0.55 ×$ Total body mass $($kilograms$)$
$2.$ Insulin also helps in disposing of carbohydrates in the human body.
In Prakhar’s body, $14.5$ insulin units dispose of $290$ grams of carbohydrate.
How many grams of carbohydrates are disposed of by $1$ insulin unit$?$
$A. 200$
$B. 20$
$C. 2$
$D. 0.2$

Answer

$4. 44$ or $44$ units
$5. B. 20$

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Question 54 Marks

Shalini, Amber and Anant have dinner together. The bill for the dinner is $Rs.3277.50.$
They divide it among themselves.
$1.$ Shalini pays first, she rounds her share amount to the nearest tens.
Amber pays next, he rounds his share amount to the nearest rupees.
The remaining amount is paid by Anant.
What is the amount paid by Anant$?$
$2.$ They have some starters, some drinks and the main course in the dinner.
One-third of the bill was for drinks and one-ifth for starters.
What amount is paid for the main course?
$A. Rs 409.68$
$B. Rs 1092.50$
$C. Rs 1529.50$
$D. Rs 1748.00$
$3.$ During the dinner, they have six glasses of drinks. Amber has one-half of them and Shalini has one-third of them. Anant has rest of them.
How many glass/es does Anant have$?$

Answer

1. 1095.50 or ₹ 1095.50
2. C. ₹ 1529.50
3. 1 or 1 glass

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Maths case /data -based (4 Marks)

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