Aptitude Discussion

Q. |
How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27kg of sugar costing Rs.7 per kg so that there may be gain of 10% by selling the mixture at Rs.9.24 per kg? |

✖ A. |
60 kg |

✔ B. |
63 kg |

✖ C. |
50 kg |

✖ D. |
77 kg |

**Solution:**

Option(**B**) is correct

Let the rate of second quality be Rs $x$ per Kg.

C.P of 1 Kg sugar of 1st 980p

**Step 1 :**

S.P of 1 kg of mixture = Rs. 9.24

Gain = 10%

C.P of 1 kg of mixture $=\left[\dfrac{100}{100+10}\times 9.24\right]$

$=\text{Rs. } 8.40$

$\Rightarrow$ Mean price = Rs. 8.40

**Step 2 :**

C.P of 1 kg of sugar of 1st kind = 900p

C.P of 1 kg of sugar of 2nd kind = 700p

Mean price = 840p

By the rule of alligation, we have:

C.P. of 1kg of C.P. of 1kg of

sugar of 1st sugar of 2nd

kind (900p) kind (700p)

\ /

Mean Price

(840p)

/ \

840 - 700 : 900 - 840

(140) (60)

⇒Required ratio $= 140 : 60 = 7 : 3$

**Step 3:**

Let $x$ kg of sugar of 1st kind be mixed with 27 kg of 2nd kind

\begin{align*}

7:3&=x:27\\

\Rightarrow \dfrac{7}{3}&=\dfrac{x}{27}\\

\Rightarrow x &= \left(\dfrac{7}{3}\times 27\right)\\

&=63 \text{ Kg.}

\end{align*}

**Shekhar**

*()
*

very very good explanation