NCC BANK LTD | WRITEN QUESTION(MATH)

Ashifur August 8, 2023 - 20:12

Question 1:

X sells an item to Y at a profit of 28% and Y sells the same item to Z at a loss of 25% on his cost. If Y had sold the item to Z at Tk. 2 less than what it costs to X, what is the cost of the item to X in Taka?

Answer:

50 TK

Explanation:

Let, the cost of item to X is x Tk.
Cost price on = (x x $\frac{28}{100}$+x) = 1.28x Tk
Cost price of Z = (1.28x – 1.28x x $\frac{258}{100}$) Tk
= (1.28x— 0.32) = .96x Tk
According to the question
x = 0.96x + 2
=>x — 0.96x = 2
=>0.04x = 2
x = 50 Tk

Question 2:

2 men and 5 women completed only $\frac{1}{4}$th portion of a job in 3 days. After 3 days, another man was included in the team and 2 days they completed another $\frac{1}{4}$th portion of the job. How many men (with no women) can complete the whole job in 4 days?

Answer:

6 men

Explanation:

2 men + 5 women, in 3 days complete = %$\frac{1}{4}$ portion
5 women, 1n 1 days complete =$\frac{1}{4×3}$= $\frac{1}{12}$ portion
3 men + 5 women, in 2 days complete = $\frac{1}{4}$ portion
5 women, 1n 1 days, complete =m$\frac{1}{4×2}$= $\frac{1}{8}$ portion

That is,
3 men + 5 women completes in 1 day =$\frac{1}{8}$ portion ————–(i)

2 men + 5 women completes in 1 day = $\frac{1}{12}$ portion ———(ii)
(i) – (ii) => 1 man complete in day =$\frac{1}{24}$ portion
$\frac{1}{24}$ portion completed in 1 day by = 1 man

1 portion completed in 1 day by = 24 x 1 man

1 portion completed in 4 day by =$\frac{24}{4}$ = 6 men

Question 3:

Mr. Karim deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 45,000 when the ratio of interest and investment became 2: 5. If the interest rate was 3.6%, calculate the time period for which the money was invested.

Answer:

11.11 years

Explanation:

Here, R = 3.6 and T =?

Let,
interest, 1 = 2x
investment, P = 5x
Total amount = 2x + 5x = 7x
According to the question,
7x = 45000
x = 6428.57
Investment, P = 5x = S x 6428.57 = 32142.85Tk
Interest, I = 2x = 2 x 6428.57 = 12857.14Tk
Time, T = $\frac{100xI}{PR}$ = $\frac{100×12857.14}{32142.85×3.6}$
= 11.11 years

Question 4:

A football team has a ratio of win to loss of 3 : 1. After winning 6 games in a row, the team’s ratio of win to loss became 5 : 1. How many games had the team won before it played the last six games?

Answer:

9 Nos

Explanation:

Let, the number of wining game be 3x
The number of losing games be x
According to the question,
3x + 6 : x = 5 : 1 $\frac{3 x + 6}{x}$

=> 2x = 6
x = 3
The team won before it played the last six games = 3x = 3 x 3 = 9

Question 5:

Coffee A normally costs 100 taka per pound, It is mixed with coffee B, which normally costs 70 taka per pound, to from a mixture which cost 80 taka per pound. if there are 12 pounds of the mix, how many pounds of coffee A are used in the mix?

Answer:

4 pounds

Explanation:

Let, the amount of coffee A is 1: pound

So the amount of coffee B = 12 —x pound
Cost of A =x x 100 = 100x Tk.

Cost of B = (12 —x) x 70 = (12 —x) 70 Tk.
Cost of mixture = 12 x 80 = 960 Tk.
=> 100x+ (12 —x) 70 = 960

=> 100x + 840 — 70x = 960

=> 30x = 960 — 840 = 120

x = $\frac{120}{30}$ = 4

Question 6:

An item was sold at 5% profit. If the cost was 5% less and the selling price was Tk. 5 less, then the trader would have made a profit of 10% on cost. What was the cost of the item?

Answer:

1000 TK

Explanation:

Let, cost of the item Tk. 100
At 5% profit, the selling price = 100 + 5 = 105 Tk.
At 5% less, cost = 100 — 5 = 95 Tk.
At 10% profit, the selling price = 95 + 10% of 95
= 95 + 9.5 = 104.5 Tk.
So,
Selling price difference is Tk. 0.5 when previous cost = 100 Tk.
Selling price difference is Tk. 5 when previous cost = $\frac{100×5}{0.5}$= 1000 Tk.

X sells an item to Y at a profit of 28% and Y sells the same item to Z at a loss of 25% on his cost. If Y had sold the item to Z at Tk. 2 less than what it costs to X, what is the cost of the item to X in Taka?

2 men and 5 women completed only $\frac{1}{4}$th portion of a job in 3 days. After 3 days, another man was included in the team and 2 days they completed another $\frac{1}{4}$th portion of the job. How many men (with no women) can complete the whole job in 4 days?

Mr. Karim deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 45,000 when the ratio of interest and investment became 2: 5. If the interest rate was 3.6%, calculate the time period for which the money was invested.

A football team has a ratio of win to loss of 3 : 1. After winning 6 games in a row, the team’s ratio of win to loss became 5 : 1. How many games had the team won before it played the last six games?

Coffee A normally costs 100 taka per pound, It is mixed with coffee B, which normally costs 70 taka per pound, to from a mixture which cost 80 taka per pound. if there are 12 pounds of the mix, how many pounds of coffee A are used in the mix?

An item was sold at 5% profit. If the cost was 5% less and the selling price was Tk. 5 less, then the trader would have made a profit of 10% on cost. What was the cost of the item?

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