## RS Aggarwal Class 6 Math Tenth Chapter Ratio, Proportion And Unitary Method Exercise 10D Solution

## EXERCISE 10D

**OBJECTIVE QUESTIONS**

**Mark (√)**** against the correct answer in each of the following:**

**(1) The ratio 92 : 115 in its simplest form is**

**Ans: (d) 4 : 5**

92 : 115

=92115=92÷23115÷23=45

= 4 : 5

**(2) If 57 : x : : 51 : 85, then the value of x is**

**Ans: (a) 95**

51×x=57×85

or,x=484551=95

**(3) If 25 : 35 : : 45 : x, then the value of x is**

**Ans: (a) 63**

25×x=35×45

or,x=157525=63

**(4) If 4 : 5 : : x : 35, then the value of x is**

**Ans: (c) 28**

5×x=4×35

or,x=1405=28

**(5) If a, b, c, d are in proportion, then**

**Ans: (b) ad**** = bc**

Here, we can write a : b : : c : d

We know that, Product of extremes = Product of means

**(6) If a, b, c are in proportion, then**

**Ans: (b)**

** **

Here, we can write a : b : : b : c

We know that, Product of extremes = Product of means

**(7) Choose the correct statement:**

**Ans: (b) (5 : 8) < (3 : 4)**

**(8) If Rs 760 is divided between A and B in the ratio 8 : 11, then B’s share is**

**Ans: (a) Rs 440**

Total money = Rs 760

Sum of ratio term = (8 + 11) = 19

B’s share=Rs760×1119=Rs440

**(9) Two numbers are in the ratio 5 : 7 and the sum of these numbers is 252. The larger of these numbers is**

**Ans: (d) 147**

let the number required number is x.

So,5x+7x=252or,12x=252or,x=25212or,x=21

Hence the largest number is (7 x 21)=147.

**(10) The sides of a triangle are in the ratio 1 : 3 : 5 and its perimeter is 90 cm. The length of its largest side is**

**Ans: (b) 50 cm**

Let the required number is x cm.

So,1x+3x+5x=90or,9x=90or,x=909or,x=10

Hence the largest side is (5 x 10) = 50 cm.

**(11) The ratio of boys and girls in a school is 12 : 5. If the number of girls is 840, the total strength of the school is**

**Ans: (c) 2856**

Let the required students of the school is x.

So,5x=840or,x=8405or,x=168

Hence, the total strength is (12 x 168 + 840) = 2856.

**(12) If the cost of 12 pens is Rs 138, then the cost of 14 such pen is**

**Ans: (b) Rs 161**

**(13) If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?**

**Ans: (b) 45 days**

**(14) If 40 men can finish a piece of work in 26 days, how many men will be required to finish it in 20 days?**

**Ans: (a) 52**

**(15) In covering 111 km, a car consuming 6 L of petrol. How many kilometers will it go in 10 L of petrol.**

**Ans: (b) 185 km**

**(16) In a fort, 550 men had provisions for 28 days. How many days will it last for 700 men?**

**Ans: (a) 22 days**

**(17) The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is **

**Ans: (c) ****90 ^{o}**

Let the required angle is x^{o}

So,3x+1x+2x=180or,6x=180or,x=1806or,x=30

Hence, the largest angle is (3 x 30) = 90^{o}

**(18) Length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?**

**Ans: (b) 45 m**

Let the length of the field is x m.

So,4x=36or,x=364or,x=9

Hence, the length is (5 x 9) = 45 m.

**(19) If a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours, then the ratio of their speeds is**

**Ans: (a) 13 : 15**

195 km : 3 h = 195 : 3

=1953=65

300 km : 4 h = 300 : 4

=3004=75 Hence,65:75=65÷575÷5=1315=13:15

**(20) If the cost of 5 bars soap is Rs 82.50, then the cost of one dozen such bars is **

**Ans: (c) Rs 198**

**(21) If the cost of 30 packets of 8 pencils each is Rs 600, what is the cost of 25 packets of 12 pencils each?**

**Ans: (b) Rs 750**

**(22) A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?**

**Ans: (a) Rs 344**

**(23) The 1st, 2nd and 4th terms of a proportion are 12, 21 and 14 respectively. Its third term is **

**Ans: (d) 8**

Let the third term is x.

So,21×x=12×14or,x=16821or,x=8

**(24) 10 boys can dig a pitch in 12 hours. How long will 8 boys take to do it?**

**Ans: (b) 15 h**