Question

1. (a) Arun spends some of the money from his monthly salary on food, travelling
and entertainment and the rest of the money he deposits in the bank.

(i) The money he spends on food, traveling, and entertainment is in the
Ratio, food : travelling : entertainment = 4 : 2 : 3.
If he spends on food $160 more than traveling calculate the amount he
spends on entertainment.
Answer(a)(i) $ ................................................ [2]
(ii) Find the total amount he spends on food, travelling and entertainment.
Answer(a)(ii) $............................................ [2]
(iii) If he deposits 1
7
of his monthly salary, calculate his monthly salary.
Answer(a)(iii) $............................................ [2]
2
[ Turn Over
(b) The bank pays 4.8% simple interest per year for the money that he
deposits in the bank.
Find the total amount he will get after 3 years.
Answer(b) $ ................................................ [2]
(c) Next month he got a salary increment and he received $ 900 for his salary.
Calculate the percentage increase in salary.
Answer(c) .................................................% [3]

Answer 1

Given :- Arun spends some of the money from his monthly salary on food, travelling and entertainment and the rest of the money he deposits in the bank. The money he spends on food, travelling and entertainment is in the Ratio, food : travelling : entertainment = 4 : 2 : 3. If he spends on food $160 more than travelling.

To Find :-

1. Calculate the amount he spends on entertainment.
2. Find the total amount he spends on food, travelling and entertainment.
3. If he deposits $17 of his monthly salary, calculate his monthly salary.
4. The bank pays 4.8% simple interest per year for the money that he deposits in the bank. Find the total amount he will get after 3 years.
5. Next month he got a salary increment and he received $ 900 for his salary. Calculate the percentage increase of the salary.

Solution :-

Let us assume that, The money he spends on food, travelling and entertainment is 4x , 2x and 3x .

So,

→ Food - Travelling = $160

→ 4x - 2x = 160

→ 2x = 160

→ x = $80 .

then,

→ Amount he spent on entertainment = 3x = 3 * 80 = $240 (Ans. 1)

and,

→ The total amount he spends on food, travelling and entertainment = (4x + 2x + 3x) = 9x = 9 * 80 = $720 (Ans. 2)

now , he deposit rest $17 in bank .

Therefore,

→ Monthly salary of Arun = $720 + $17 = $737 (Ans. 3)

Now,

Principal added per month = $17

Rate = r = 4.8% = (4.8/100) = 0.048 .

Time = N = 3 years.

k = 12 months .

A = Total amount after 3 years.

So, by annuity formula, we get,

→ A = P{(1 + r/k)^(N•k) - 1} / (r/k)

→ A = 17•[{1 + (0.048/12)}^(12*3) - 1] / (0.048/12)

→ A = 17•[(1 + 0.004)³⁶ - 1] / (0.004)

→ A = 4250[(1.004)³⁶ - 1]

→ A = 4250 * (1.154 - 1)

→ A = 4250 * 0.154

→ A = $654.5 (Ans. 4)

Now,

→ Next month he recieved = $900 .

So,

→ Increment in monthly salary = 900 - 737 = $163 .

then,

→ % increase in monthly salary = (163 * 100) / 737 = 22.11 % (Ans. 5)

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