Solve the following problems:

Created: 3 years ago | Updated: 10 months ago

Updated: 10 months ago

Dhaka Bank Dhaka Bank AO - 2021 গণিত 2021

267

The cost of operating a Frisbee company in the first year is $10,000 plus $2 for each Frisbee. Assuming the company sells every Frisbee it makes in the first year for $7, how many Frisbees must the company sell to break even?

উত্তরঃ

$L e t, t h e c o m p a n y m u s t s e l l x n u m b e r o f F r i s b e e t o m a k e b r e a k e v e n .$

$A c c o r d i n g t o q u e s t i o n$

$7 x = 10000 + 2 x$

$= 7 x - 2 x = 10000$

$= 5 x = 10000$

$∴ x \frac{10000}{5} = 2000$

The company must sell 2,000 Frisbee to make break even.

PRONAY TIRKI

2 years ago

(b)

Frank scored 26 points in a basketball game. All of his points came from either a two-point or three-point basket. If frank scored at least one three-point basket, what is the maximum number of two-point baskets that Frank could have scored?

উত্তরঃ

$L e t, x b e t h e m a x i m u m n u m b e r o f t w o p o i n t s .$

According to question

$2 x + (2 \times 3) = 26$

$= 2 x + 6 = 26$

$= 2 x = 26 - 6 = 20$

$∴ x = \frac{20}{2} = 10$

PRONAY TIRKI

2 years ago

(c)

There are three pumps P, Q and R with a tank. P. Q and R simultaneously can fill the tank in 5 hours. Again P and Q simultaneously can fill the tank in 7 hours. Then how many hours R need to fill the tank alone?

উত্তরঃ

$(P + R + T) t a k e 5 h o u r s t o f i l l u p 1 \tan k$

$∴ (P + R + T) t a k e 1 h o u r t o f i l l u p \frac{1}{5} p a r t o f \tan k$

$A g a i n, (P + R) t a k e 7 h o u r s t o f i l l u p 1 \tan k$

$∴ (P + R) t a k e 1 h o u r t o f i l l u p \frac{1}{7} p a r t o f \tan k$

$∴ I n 1 h o u r, T c a n f i l l u p = (\frac{1}{5} - \frac{1}{7}) = \frac{7 - 5}{35} = \frac{2}{35} p a r t o f \tan k$

$N o w, \frac{2}{35} o f \tan k i s f i l l e d b y T i n 1 h o u r$

$∴ 1 o r c o m p l e t e p a r t o f \tan k i s f i l l e d b y T i n = \frac{35 \times 1}{2} = 17 \frac{1}{2} h o u r s$

PRONAY TIRKI

2 years ago

(d)

There is equal number of students in each of 10 classes in a school. In a day with bad weather, three classes are 1/2 full, 5 classes are 3/4 full and two classes 1/6 th empty. If the number of absent 6 students is 74 in that particular day, what is the total number of students in 10 class?

উত্তরঃ

$L e t, x b e t h e t o t a l n u m b e r o f s t u d e n t s i n e a c h c l a s s .$

$∴ 10 x w i l l b e t h e n u m b e r o f t o t a l s t u d e n t s$

$H e r e, n u m b e r o f a b s e n t i n 3 c l a s s = x - \frac{x}{2} = \frac{x}{2}$

$N u m b e r o f a b s e n t i n 5 c l a s s = x - \frac{3 x}{4} = \frac{4 x - 3 x}{4} = \frac{x}{4}$

$∴ N u m b e r o f a b s e n t i n 2 c l a s s = \frac{x}{6}$

$A c c o r d i n g t o q u e s t i o n (3 \times \frac{x}{2}) + (5 \times \frac{x}{4}) + (2 \times \frac{x}{6}) = 74 = \frac{3 x}{2} + \frac{5 x}{4} + \frac{x}{3} = 74 = \frac{18 x + 15 x + 4 x}{12} = 74 = 37 x = 74 \times 12 ∴ x = \frac{74 \times 12}{37} = 24 H e n c e, t o t a l s t u d e n t s = 10 * 24 = 240$