Chain rule problems with solutions for SSC and Bank Exams

Every question has a solution. Some student has found the solution and some are unable to find a solution. Same as chain rule problems have solutions but some students face difficulty in solving chain rule problems. So, here you can easily learn how to solve chain rule problems with solutions for SSC and bank exams.

You can increase your chances of success in the competitive exams with the help of these chain rule problems with solutions because the same questions asked in competitive exams like as examples of here.

You can practice also chain rule questions and answers after complete your learning process.

Chain rule problems with solutions for Competitive Exams

Q.1.If 15 toys cost Rs. 234, what do 35 toys cost?

Solution. 

Let the required cost be Rs. x. Then,

More toys, More cost              (Direct Proportion)

∴ 15 : 35 :: 234 : x ↔ (15 × x) = (35 × 234)  $$   ↔\ x =  \left({35×234\over15}\right)= 546 $$ 

Hence, the cost of 35 toys is Rs 546

Q.2. If the wages of 6 men for 15 days-be Rs. 2100, then find the wages of 9 men for 12 days.

Solution. 

Let the required wages be Rs. x.

More men, More wages            (Direct Proportion)

Less days, Less wages              (Direct Proportion)

 : : 2100 : x

∴ (6 × 15 × x ) = (9 × 12 × 2100) $$  ↔\ x =   \left({9×12×2100\over6×15}\right)= 2520 $$

Hence, the required wages are Rs. 2520.

Q.3. If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?

Solution. 

Let the required number of days be x.

More men, Less days                         (Indirect Proportion)

Less hours per days, More days      (Indirect Proportion)

 :: 16 : x

∴ ( 18 × 8 × x) = ( 15 × 9 × 16) $$  ↔\ x =  \left({15×144\over144}\right)= 15 $$

Hence, required numbers of days = 15.

Q.4. If the price of 6 toys is Rs. 264.37, what will be the approximate price of 5 toys?

Solution. 

Let the required price be Rs. x. Then, Less toys, Less cost (Direct Proportion) 

∴ 6 : 5 : : 264.34 : x ↔ ( 5 × 264.37) $$  ↔\ x =   \left({5×264.37\over6}\right)x= 220.308 $$

∴ Approximate price of 5 toys = Rs. 220

Q.5.A fort had the provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is  

Solution. 

After 10 days: 150 men had food for 35 days.

Suppose 125 men had food for x days. Now, Less men, More days (Indirect Proportion)

∴ 125 : 150 : : 35 : x ↔ 125 ×  x = 150 × 35  $$  ↔\ x =  \left({150×35\over125}\right)x= 42 $$

Hence, the remaining food will last for 42 days.

Q.6. If 36 men can do the piece of work in 25 hours, in how many hours will 15 men do it?

Solution. 

Let the required number of hours be x. Then,

Less men, More hours        (Indirect Proportion )

∴ 15 : 36 : : 25 : x ↔ (15 × x) = ( 36 x 25)  $$  ↔\ x =  \left({36×25\over100}\right)= 60 $$

Q.7. If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days ?

Solution. 

Let the required number of days be x metres

More men, More length built                        (Direct Proportion)

Less days, Less length built                          (Direct Proportion

: : 56 : x

∴ ( 20 × 6 × x ) = ( 35 × 3 × 56) $$  ↔\ x =   \left({35×3×56\over120}\right)= 49 $$

Hence, the required length is 49 m.

Q.8.  If the cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?

Solution. 

Cost of x meters = Rs.d. Cost of 1 meter = Rs. $$   =   Rs\left({d\over x}\right) $$

Cost of y meters   $$    =  Rs\left({d\over x}×y\right)=  Rs\left({yd\over x}\right) $$

Q.9. 36 men can complete a piece of work in 18 days. In how many more days will 27 men complete the same work ?

Solution. 

Let the required number of days be x.

Then, Less men, More days (Indirect Proportion)

∴ 27 : 36 :: 18 : x ↔ 27 × x. ↔ 27 ×  x = 36 × 18  $$   ↔\ x =   \left({36×18\over27}\right)x= 24 $$

Q.10. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolution made by the larger wheel is : 

Solution. 

Let the required number of revolution made by larger wheel be x.

Then, More cogs, Less revolution ( Indirect Proportion)

∴ 14 : 6 : : 21 : x ↔ 14 ×  x = 6 × 21 $$  ↔\ x =   \left({6×21\over14}\right)= 9. $$

With the help of these 10 solutions, you can take an idea to solve the chain rule problems which will help you in your competitive exams. You can ask me in the comment section if you have any doubt regarding chain rule problems with solutions.