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Mathematical Problems (Show your steps/calculation)

A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution?

Let, x units of 12% acid needs to be mixed with.

According to question

x $\times$ 12% +400 $\times$ 6% = (400+x) $\times$ 10%

$= \frac{12 x}{100} + \frac{400 \times 6}{100} = \frac{(400 + x) \times 10 %}{100} = 12 x + 2400 = 4000 + 10 x [M u l t i p l y i n g b o t h s i d e s b y 100] = 2 x = 1600 ∴ x = \frac{1600}{2} = 800 A n s w e r : 800 u n i t e s o f 12 % a c i d n e e d s t o b e m i x e d .$

Mathematical Problems (Show your steps/calculation)

A school store sells only one kind of pen and pencil at a uniform price per pen or per pencil. If the cost of 3 pens and 6 pencils is twice that of 12 pens and 4 pencils, then the total cost of 2 pens and 4 pencils is how many times that of one pen?

Let, the price of pen and pencil be x Tk. and y Tk. respectively.

According to question =

2(3x+6y)=12x+4y

=6x+12y=12x+4y

=6x=8y

$∴$ y= $\frac{6 x}{8} = \frac{3 x}{4} . . . . . . . . . . . . . (i)$

$∴$ 2 pens and 4 pencils cost

=2x+4y

=2x+4 $\times \frac{3 x}{4}$

=2x+3x

=5x

That means 2x+4y=5x

i.e. the total cost of 2 pens and 4 pencils is equal to the 5 times of one pen.

Job Solution | United Commercial Bank Ltd (UCB)

United Commercial Bank Ltd. || Probationary Officer (03-01-2020) || 2020

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