Please explain these few questions properly, step by step 1)55% of students in a school are boys and - Maths - Comparing Quantities

Question

Please explain these few questions properly, step by step

1)55% of students in a school are boys and the number of girls are
810 Find the total number of students and the number of girls
2)Find a number which:
i) When increased by 10% becomes 77
ii) When increased by 8% becomes 115

3)Aditya's income is 20% less than that of Arnav How much percent
is Arnav's income more than Aditya's income?
4)The price of sugar increases by 20% By what percentage should a
housewife reduce consumption so that her expenditure does not
increase?
5)At what rate percent will a sum of money double itself in 8
years?

Please explain properly! Thankyou

Manmeet Singh · Accepted Answer

Due to paucity of time, we are unable to solve all your queries. We are solving some of them.

Q1. The answer posted by @Shivangi64 for the first part is correct. Keep it up Shivangi. Continue the hard work.

Q3. Let Arnav`s income be 100.

So, Aditya`s income = $100 - \frac{20}{100} \times 100 = 100 - 20 = 80$

Arnav`s income is 20 more than that of Aditya`s = $\frac{20}{80} \times 100 = 25 %$

Q4.

Expenditure = consumption × price

Let price of sugar be 100

Expenditure = consumption × 100

Consumption = $\frac{\exp e n d i t u r e}{100}$

⇒expenditure = 100 × consumption 1

When the price of sugar increases by 20%,

the new price = 100 + 20%(100) = 100 + 20 = 120.

Expenditure = 120 × consumption 2

Since the consumption remains constant,

100 × consumption 1 = 120 × consumption 2

⇒ consumption 2 = $\frac{10}{12} = \frac{5}{6}$ consumption 1

Thus, the decrease in consumption = $\frac{1 - \frac{5}{6}}{1} \times 100 = \frac{1}{6} \times 100 = 16.66 %$

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